How The Media Misled The Public About Who Was Behind The Attack On Al-Ahli Hospital

A crime is committed. The police are notified. When the police arrive at the crime scene, they find two suspects holding guns. 

The first suspect is a dear friend of the victim. The second suspect is a fierce enemy of the victim.

The former suspect was holding a rudimentary gun while the latter suspect was carrying a sophisticated one.

The former suspect was known to have defended the victim on multiple occasions. The latter suspect is known to have killed thousands of people with similar profiles before. Even worse, he always denied responsibility despite proven otherwise.

For five days in a row before the crime took place, this fierce enemy repeatedly threatened to kill the victim. Three days before the crime was committed, he shot a bullet at the victim that caused the latter a non-life threatening injury.

After a brief questioning, the police release the fierce enemy of the victim while detaining the dear friend, charging him with a first-degree murder.

A movie thriller? Not really.

This is precisely what happened after the horrific massacre that took place at the Al-Ahli Hospital on the night of October 17, 2023: The majority of the investigations conducted by Western media laid the blame on a misfired Hamas/Jihad rocket.

These investigations took place within days following the attack. Some of them were updated a few weeks after the incident to correct a finding that was made in the initial investigation.

The Al-Jazeera footage shown below is the one the media depended on to reach their earlier [now erroneous] conclusion.

Video # 1: Al-Jazeera footage showing the explosion and the midair interception of a Hamas rocket

In the above footage, we see an object that rises vertically. Seconds later, it changes direction twice before exploding around the 13th-second. A second and a third explosion take place on the ground, 5 seconds and 7 seconds later, respectively.

The bulk of the earlier media investigations concluded that this rising and then exploding object was a Hamas rocket that disintegrated midair before moving on to land in the hospital courtyard a few kilometers away. This explanation was supported by American, British, French, and Canadian intelligence.

This early finding reached by the media, after consulting a few military experts, is scandalous for the following reasons:

1- It is well known that a Hamas rocket doesn’t possess any guidance capabilities. So it is very unlikely for such a rudimentary rocket to change direction twice. Changing directions is a feature of interceptor missiles like the Iron Dome ones (see Video # 2 below, where you can watch Iron Dome missiles changing directions to intercept Hamas missiles).

2- Hamas rockets burn their fuel within the first few seconds after launch. The firelight tail typically disappears after that initial phase (called the boost phase). The object in the video keeps showing a firelight tail for 10 seconds or more before exploding (the camera starts capturing the object while it was already in the air).

3- Based on 2 above, there is no way a Hamas rocket would have contained fuel by the time it reached the hospital. Even if it did, the midair explosion would have evaporated most, if not all, the fuel remaining.

4- When Hamas or Jihad fires rockets, they do fire them in batches, say 10-20 rockets within a span of 20-30 seconds. We see no other object being fired from the same site. This should have been considered a flag the rising object was not a Hamas rocket.

5- Unlike this object, that is rising at a 90° degree angle, Hamas artillery rockets are launched at an angle of about 30° to 60°.

6- Even if the explosion took place right above the hospital, laws of physics dictate that at that height of more than 4 Km the debris would have taken much more time than 7 seconds to reach the ground.

How could the consulted military experts have ignored these simple known facts? It looks like there either was a clear bias (and haste) to blame Hamas/Jihad for the attack or these experts knew little about Qassam rockets and their Iron Dome interceptors.

Video # 2: Iron Dome missiles intercepting Hamas rockets

In subsequent updates, the media retracted their claim and admitted the rising and then exploding object was in fact an Iron Dome missile that was launched from inside Israel. They still insisted the object that hit the hospital was a Hamas rocket.

Our investigation demonstrates that this hastily reached conclusion is incorrect. Our main findings in this report are:

1- Using physics, mathematics, and the location of the rocket launch site with respect to the hospital, the object that hit the hospital could not have been a Hamas rocket.

2- Using physics, mathematics, we demonstrate that the weapon that was used to target the hospital was most likely launched from an aircraft that was approaching the hospital from the northwest direction.

The media investigations

Here’s a list of the most prominent investigations that took place:

1- The Associated Press Nov 22 investigation (an update on the Oct 21 one).

2- The New York Times Oct 31 investigation (an update on the Oct 24 one).

3- The Washington Post Oct 26 investigation.

4- The Wall Street Journal Oct 22 investigation.

5- Le Monde Nov 3 investigation

6- Al-Jazeera Oct 19 investigation.

7- The Channel 4 Oct 21 investigation.

Aside from the Channel 4 and Al-Jazeera investigations (investigation # 6 and # 7), all other investigations concluded a misfired Hamas/Jihad rocket was to be blamed.

While they later admitted they had wrongly interpreted the above Al-Jazeera footage (based on other video footage obtained), investigations # 1-5 insisted, in a later followup update, the object that hit the hospital was a Hamas rocket. Their insistence to stick to the initial conclusion (confirmation bias?) was mainly based on the size of the crater the missile/rocket caused in the courtyard of the hospital, which they claimed was too small to be caused by any of the bombs the IDF were dropping in Gaza.

It should be pointed out that the last two investigations (investigation # 5 and # 6) made an innocent mistake: They concluded the object that hit the hospital could have only originated from the east of the hospital (i.e. from Israel), and therefore the possibility of a Hamas/Jihad rocket being behind the blast is ruled out (as it was established beyond reasonable doubt the rocket launch site was located southwest of the hospital).

The conclusion reached by these two investigations was based on a Doppler shift analysis conducted by Earshot and Forensic Architecture, two open-source organizations that specialize in audio and video analysis. These two organizations used a standard [rudimentary] 2D model to compute the Doppler shift. This simple model ignores the elevation [vertical] angle which, like the azimuth [horizontal] angle, has an impact on the Doppler shift caused by the moving object.

The study conducted by Michael Kobs has a much more rigorous analysis where a more realistic 3D model was used. In his report, he demonstrates that the projectile most likely originated from the northwest direction at an angle of 35° when compared with the axis of the camera shown later in Video # 9. We will see later that this 35° angle coincides well with where the two IDF aircraft were approaching the hospital from.

What I want to highlight here is that the above investigations either ignored or downplayed the significance of the presence of two IDF aircraft flying above the vicinity of the hospital at the time of the explosion

What I want to highlight here is that these investigations either ignored or downplayed the significance of the presence of two IDF aircraft flying above the vicinity of the hospital at the time of the explosion.

The Le Monde investigation mentioned the presence of these two aircraft but stopped short of pursuing the possibility of one of these aircraft being behind the attack on the hospital. They also falsely stated the two aircraft made a left turn and didn’t enter the city. This is contradicted by the Bat Yam footage, as we shall see later.

The Human Rights Watch report

In late November 2023, Human Rights Watch (HRW) published a report in which the organization suggested the weapon that hit Al-Ahli Hospital was most likely a Hamas rocket.

Contrary to public perception, the organization did not reach a definitive conclusion but rather left the door open by stating “while misfires are frequent, further investigation is needed to determine who launched the apparent rocket”.

HRW’s experts suggested the whistling sound the flying object produced as it was approaching the hospital was consistent with the sound of a rocket. It is unclear whether the HRW team conducted sound analysis (as we do here) in order to arrive at this conclusion. One needs not to be an expert to judge their finding on the sound issue is incorrect. By simply listening to the sound signature of a falling MK-82 bomb fitted with a JDAM guidance tail kit, for example, one finds a striking resemblance between this whistle sound and the whistle sound of the object that hit the hospital.

Another aspect of the explosion that was highlighted in the report is the small size of the crater that was caused by the impact. It is indeed true that Hamas rockets cause much smaller craters when compared to craters caused by large bombs like the MK-82 or the MK-84 ones. But this doesn’t exclude the possibility that Israel used smaller bombs to attack the hospital. For example, the GBU-39A/B bomb weighs only 129 kg and its lethality can be programmed ahead of time.

The report, in an attempt to explain the higher than usual damage by a Hamas rocket, suggests that Hamas could have used a much larger rocket on that night. The report further states that the rocket could have contained unspent fuel at the time of the explosion. First, why would Hamas use a long-range multi-stage missile to target a nearby city like Sderot (the target of the rockets on that night)? Second, it is evident from the video evidence that the rockets spent their fuel only seconds after launch (they were a few kilometers away from the hospital when they ran out of fuel). Third, if one were to assume a big rocket was launched not far away from the hospital (say from the nearby cemetery) and failed immediately, why don’t we see any firelight in any of the multiple video footage?

The other explanation that was suggested in the report based on a video clip the HRW team has watched (we found no such video) is the presence of a cooking gas cylinder inside one of the parked cars. Even if true, a cylinder of this size has the same destructive power as a few hand grenades and would definitely not cause the entire courtyard to burn and for a car to flip.

Contrary to the claim made in the report, all the fireballs that were generated by the three explosions, including the hospital one, are in fact similar. What’s more: an IDF aircraft emptied its load an hour after the hospital explosion on an area that is located south of the hospital (see Appendix). That fireball is also similar. This suggests that all those fireballs were caused by either similar bombs or by similar Hamas rockets. This last suggestion is impossible unless we assume the IDF aircraft were simply having a picnic above Gaza City.

The report acknowledges the presence of two IDF aicraft within the vicinity of the hospital around the time of the explosion. However, it does fail to pursue the possibility of any of them being behind the attack. For example, it is well known that there is a time correlation between when an aircraft fires decoys and when it releases its load. The HRW team rightly states this happened 32 seconds before the hospital explosion. Had they taken the next step, they would have found out that the release of the load from that distance, at that time and at that height, would have reached the hospital in time to cause the explosion.

One last criticism of the report is that the team has not conducted proper triangulation. It is not clear how many and which video footage they had evaluated. This leads the reader to suspect the investigation was not rigorous enough.

Location of the rocket launch sites

The various published media investigations agree with the map released by the IDF on Oct 18. The map, shown below, locates three rocket launch sites. Of importance to our investigation is the location of the southwest launch site (big red ball).

Using Google Maps, we find this launch site is located about 5 Km southwest of the hospital. The other two launch sites (small gray balls) are located northeast and northwest of the hospital (they were firing northeast, most likely toward Ashkelon and Tel Aviv). So the hospital was not in their path.

Image # 1: A map suuplied by the IDF that shows the three rocket launch sites

Our triangulation lends credibility to this IDF map. We find the map does indeed reflect the approximate positions of the three launch sites.

It should be noted that the IDF first claimed the rocket was fired from a cemetery near the hospital. They later retracted their claim and published this map, stating the rocket was fired from a launch site located southwest of the hospital (the one marked by the red ball).

We triangulated the various site locations using multiple video footage. The map below shows the southwest site (pink ball), the hospital (the red mark), the distance to the hospital, and the distance to Sderot city center (the target of the rockets). Also shown are possible directions for the rockets, delimited by the north and south of Sderot’s city limits (the dotted blue arrows). 

Map # 1: The location of the southwest rocket launch site with respect to the hospital. Also shown are the distance to Sderot, the location of the Iron Dome launch site and the location of the midair interception of a Hamas rocket.

From the above, we can easily see that the hospital was not far away from the paths that any of the rockets launched on the night of October 17 could have taken.

On the horizontal plane, the closest path would approximately be 500 m from the hospital, and the farthest one would approximately be 1.5 Km away.

So it is rather plausible that at least one of the rockets could have flown towards the hospital and landed in its courtyard.

What is also interesting to note is that the first and second explosions that took place are more likely to be the result of a Hamas rocket misfiring than the hospital one. This is because the locations of these explosions lie within the horizontal angular range these rockets were firing at.

Start and end times of the barrage of rockets

The Washington Post article states that the barrage of Hamas/Jihad rockets started at 44 seconds (correct) and ended at 25 seconds (wrong) before the hospital explosion.

The above start and end times of the barrage of rockets were most likely extracted from the Bat Yam footage (raw footage shown below) which is located approximately 60 Km northeast of the hospital (southwest of Tel Aviv).

Video # 3: The unedited Bat Yam footage. The CCTV is located 60 Km northeast of the hospital. Note that the clip is falsely labeled as being filmed in Ashdod.

The vast distance between the hospital and the Bat Yam camera makes it almost impossible to pinpoint the exact moment when the first and last rockets were launched. This is because:

1- The footage resolution is not high enough to allow for any proper zooming.

2- The earth curvature effect starts kicking in after 20 km, therefore preventing us from making an accurate calculation (we assume a building height of 30 m where the CCTV was located).

Another issue that arises, by only considering the Bat Yam footage, is the inability to attribute a certain rocket to any of the two, or even potentially three, launch sites (i.e. the three sites shown in Image # 1). This is because these launch sites happen to be in the same line of sight (this is mainly due to the vast distance between the camera and the launch sites).

The Channel 12 camera footage from Netivot (raw footage shown below), located 16 km southeast of the hospital, can assist in refining the accuracy of the start and end times.

Video # 4: The unedited Netivot video footage. The camera is located 16 Km southeast of the hospital.

It is important to mention that two other explosions happened seconds before the explosion at the hospital took place. According to our triangulation technique, both of these explosions are located southeast of the hospital.

Start Time

Let us start with finding the start time of the barrage. To synchronize both video clips, let us take the moment the first explosion happened as a reference. Luckily, this first explosion is captured in both clips.

Using the Bat Yam footage, one can find that the first explosion happens at the 22nd-second into the video. The second explosion happens at the 44th-second and the third explosion (the hospital one) happens at the 46th-second. 

The same first explosion happens at the 43rd-second into the Netivot footage. The video is not long enough to show the second and third explosions.

The Bat Yam footage shows the first rocket was launched 2 seconds into the footage, that is 44 seconds before the hospital explosion. From this footage, one can’t tell whether this first rocket was launched from the southwest or the northwest launch sites.

The Netivot footage clearly shows two separate launch sites. The rockets being launched from the northwest are visible between the 30th-second and 34th-second of the footage. The rockets being launched from the southwest are visible between the 25th-second and the 42nd-second of the footage.

The Netivot footage does not capture the exact moment the first rocket was launched (most likely a few seconds before the 25th-second). In this case, we have no choice but to rely on the Bat Yam footage for the start time, which is 44 seconds before the hospital explosion.

As for when the last rocket was launched, the Bat Yam footage does show some rocket activity taking place until 3 seconds before the first explosion took place.

As mentioned before, we can’t distinguish from the Bat Yam footage whether the rocket was launched from northwest or southwest of the hospital. The main reason is that they happen to be in the same line of sight as the camera.

Of prime importance to the investigation is the southwest launch site. This is because the mainstream media investigations concluded the Hamas/Jihad rocket originated from that site (the IDF also made the same claim).

From the Netivot footage, we see that the last rocket left the southwest launch site at the 36th-second, which is 7 seconds before the first explosion took place. 

If we combine this timing information with the Bat Yam one, we conclude that the last rocket was launched 7+24 = 31 seconds before the hospital explosion.

To obtain a sub-second precision, we imported all video clips into a video editor and performed a frame-by-frame analysis. We found the precise time to be 30.3 seconds.

Based on the analysis presented above, we conclude that the first rocket leaving the southwest launch site was fired approximately 44 seconds before the hospital explosion took place, and the last rocket leaving the same launch site was fired 30.3 seconds before the hospital explosion took place.

This last timestamp is crucial. It will help us determine the likelihood of a rocket hitting the hospital, as we will see later.

Below, I include the labeled versions of the two above video clips. I do that to help the reader follow the analysis presented above.

Video # 5: The labeled Bat Yam video footage
Video # 6: The labeled Netivot video footage.

It should be noted that these timing stamps can only be calculated from the raw footage (i.e. Video # 3 and Video # 4). This is because in the labeled versions, I resort to freezing the frames to draw the viewer’s attention to important moments.

Also, to be noted is that the hospital explosion that happened at 46th-second in the Bat Yam footage could barely be caught with the naked eye (a faint glare on the horizon). If you have difficulty catching the glare from that explosion, make sure to watch this video clip in a dark room.

Speed of Hamas Rockets

There is no official technical information available anywhere on the open-source Internet that says much about the speed of such rockets.

Information about the maximum range of various Qassam rockets is readily available online. The table below summarizes the various rocket arsenal Hamas possessed as of 2021.

Image # 2: The various rockets in posession of Hamas as of 2021

A mid-range Qassam rocket that has a range of 20 Km is the Q-20 rocket. This rocket could be one of the candidates that Hamas used that night, as the distance between the southwest launch site and Sderot is approximately 16 Km (from the launch site to Sdeort’s city center). It should be noted this published 20 Km range is the maximum range the rocket typically attains in favourable weather conditions.

Other missiles possessed by Hamas have a farther reach. The J90 has a maximum range of 80 Km. These long-range missiles are typically used to target cities far away like Tel Aviv. It is very unlikely long-range rockets were used on that night to target a nearby city, like Sderot.

Given the unavailability of velocity information concerning these rockets, the following question arises: Can we estimate the average and instantaneous speeds of the rockets launched on the night of October 17? 

The question is absolutely yes, as we do have enough data from various video clips to allow us to do that.

Before going into technical details, one can watch the various clips available online that show Hamas/Jihad rockets being fired from Gaza. Even a non-technical person who watches these clips realize these rockets travel at a much faster speed than a typical aircraft. The footage below is just one of many.

Video # 7: Typical speed of a Hamas rocket.

Ideal Projectile Trajectory

For this investigation, one needs not to know the full details of how unguided projectiles or rockets work. What is important to know are the basics of launching such a weapon.

Using physics, we know the maximum range of a projectile (like an artillery shell) can be reached using a launch angle of 45°, as shown below. 

A shorter distance can be attained by varying the launch angle. For instance, launching a projectile at 30° or 60° will achieve the same range as shown below.

We emphasize here that this ideal parabolic trajectory can only be achieved in the absence of air resistance. More on this topic later. 

Figure 1: Typical path taken by a projectile launched from a canon

The following two equations govern 1- the max distance d traveled by the projectile (i.e. the range) and 2- the time t it takes to travel that distance. \alpha is the launch angle in degrees and g= 9.81 m/s² is the gravitational downward acceleration. v represents the initial launch speed.

d= \frac{v^2}{g} \sin(2\alpha) \hspace{150pt} (1)

t= \frac{2v}{g} \sin(\alpha) \hspace{165pt} (2)

It must be mentioned that the trajectory of a fuel-propelled rocket differs from this parabolic trajectory only in its boost phase, which typically lasts for a few seconds at the start of the trajectory.

During this initial phase, the rocket travels almost in a straight line and only follows the above parabolic path once the fuel is completely consumed (typically within a few seconds after launch). This later phase is referred to as the coast phase.

At that moment, no more fuel remains in the rocket. This explains why we see the tail firelight only at the outset of a rocket launch. The graph shown in Figure 2 below illustrates what we have just mentioned.

Figure 2: Path taken by the rocket with (orange) and without (green) air resistance

The effect of wind in our investigation is ignored because the various video clips demonstrate the night of October 17 was relatively calm. For example, the Bat Yam footage shows the seawater hitting the shores were a bit wavy but nothing out of the ordinary. One can argue that the weather in Bat Yam, which is 60 Km away from the hospital, is not representative of what the weather was like in Gaza on that night. The audio from the Al-Jazeera cameraman (Video # 17 below) and the Netivot video clips didn’t sound windy. So our assumption to ignore the effect of wind is very reasonable, especially if one considers that a bombing mission and a rocket launching one are typically carried out when weather conditions are favourable.

As for air resistance, it acts as a drag force in the opposite direction of the motion. It is directly proportional to the speed (aka linear drag) at low speeds and directly proportional to the square of the speed (aka known as quadratic drag) at high speeds. This simply means that air friction being exercised on the rocket gets worse at higher speeds (the kind of speeds we’re dealing with here).

Air resistance tends to manifest itself in a more significant way as the rocket approaches its final destination: it dives at a sharper angle as it gets closer to the target (as in the green path shown in Figure # 2).

When using a quadratic air resistance model to include the effect of the drag force, the math gets complicated and in many cases there exists no closed-form solutions (mainly because there is now dependency between the horizontal and vertical movement), hence the need to resort to computer simulations.

Luckily, for our purposes, there exists an accurate-enough closed-form analytical model that is described by the following equation:

x(t)=x_{0}+v_{x}\tau_{c}\ln(1+\frac{t}{\tau_{c}}) \qquad (3)

\tau_{c} = \frac{m}{cv_{x}} \hspace{230pt} (4)

c = 0.5 \rho c_{d}A \hspace{182pt} (5)

x(t) \hspace{5pt} m is the horizontal distance traveled in t seconds and x_{0} \hspace{5pt} m is the initial horizontal distance. c_{d} is the drag coefficient, \rho \hspace{5pt} kg/m3 is the air density, A \hspace{5pt} m2 is the cross-sectional area of the rocket, v_{x} m/s is the horizontal velocity and m kg is the mass of the rocket. One word of caution is that the mass should only include the warhead and cylinder casing. It should exclude the weight of the fuel, as the latter would have already been consumed.

We have carried out computer simulations to confirm the accuracy of the above expression. We can confirm the model is relatively accurate for the range of parameters we are dealing with (the error is less than 500 m up to 20 Km range). When presenting the computed values later, we will present the numerical values obtained from both the analytical expression and the computer simulation.

The launch angle

We can use the video footage in our possession to estimate the launch angle. The Bat Yam video (Video # 3) shows the barrage being launched from both sites (northwest and southwest). It is also much farther away than the Channel 12 Netivot footage (Video # 4). So we will rely on the Channel 12 footage to estimate the launch angle.

The footage stabilizes at around 36 seconds into the clip. Using a protractor, we can estimate the angle to be around the 48° mark. It should be mentioned that this is the angle we see from the camera field of view (see labeled map below).

Map # 2: Projection on the Netivot camera view plane.

Using Google Maps, we can calculate the distance between the hospital and the projection on the line of site between the camera and the launch site to be 3.4 Km.

Using the triangles below along with the definition of the tangent and sinusoid we calculate the actual launch angle to be 37°.

Figure # 3: View triangle versus projection triangle.

Speed of the rocket

Of interest to our study is the last rocket launched from the southwest launch site. The main reason is this: if we can establish that the last rocket could not have hit the hospital given the speed and the 5 Km distance to the hospital, then previous rockets wouldn’t have been involved (this is because the Netivot footage clearly shows all traveled more or less at the same speed).

We import the Video # 4 footage into a video editor for better precision. We find that the last rocket was launched at 36 seconds and 6 frames into the video. Converting the number of frames to milliseconds gives us 6 frames/15= 400 ms. So the last rocket departed at 36.4 seconds into the footage.

We notice that the rocket almost follows a straight path upward until we no longer see the firelight for a brief moment, and then it reappears briefly (because of some remaining fuel) around 41 seconds and 8 frames (= 533 ms). So the rocket took 5.133 seconds to travel this boost phase transversal distance.

When we examine the 1280 x 720 resolution frame at the 41.533-second mark, we find the horizontal distance, when measured with a ruler, between the location of the rocket and the launch site to be 2.3 cm (more on the validity of this method later).

Using the same technique, we find that the horizontal distance between the launch site and the hospital is 6 cm.

This means that 2.3 cm / 6 cm x 5000 m = 1916.7 m is the horizontal distance d₁ (see Figure 2). Using the definition of cosine one finds that the transversal distance w (see Figure 2) traveled is 2400 m. Using the sinusoid definition, we find the height to be 1444.4 m (h in Figure 2).

So the average speed the rocket was traveling at is 2400 m / 5.133 s = 467.56 m/s. This speed is higher than the speed of sound (which is 343 m/s at 20° Celsius, referred to as Mach 1 using the flight science terminology). This means the average speed of the rocket was 1.36 Mach.

The average speed found above is lower than the instantaneous speed that is achieved at the moment the rocket runs out of fuel. This is because we know the rocket accelerates during the boost phase. Finding the instantaneous speed is a bit more involved (this speed is needed as it will serve as the initial launch speed in the coast phase).

Using the above ruler method, we first obtain a few data points as the rocket is accelerating upwards. Table 1 below shows the distance traveled at selected time instants (those instants were selected based on the visibility of the rocket along the upward path).

We then find a polynomial of a second degree that is a best fit for the distance traveled. We obtain the following polynomial: p(t)=47.14t^2+219.62t+23.75. Figure 4 shows the collected data curve and the best-fit polynomial curve. We clearly see the polynomial fits the distance data curve very tightly.

By using the first derivative, we obtain the instantaneous speed at any instant during the boost phase as v(t)=94.28t+219.62 . We simply substitue t= 5.13 s to obtain an instantous speed of 703.28 m/s (= 2.05 Mach). The second derivative gives the acceleration during the boost phase. It is 94.28 m/s2.

t (s)00.61.662.733.84.865.13
w (m)0208.69521.72939.11565.22191.22400
Table 1: Traveled transversal distance during the boost phase.
Figure 4: Best fit polynomial for the transversal distance traveled by the rocket.

Two legitimate questions arise here as to the validity of using this ruler method to calculate the speed of the rocket:

1- The path between the launch site to the hospital is not parallel to the camera axis.

2- The camera is not fully stabilized between the 36th-second and 41st-second timestamps.

Concerning the first question, if we project any point along the horizontal path from the launch site to the hospital onto the camera plane, the ratio between the distance traveled to the entire distance will remain the same. Using the figure below, this means d₂ / d₁ = d₄ / d₃.

Figure 5: A top view of the projection on the ground plane.

Concerning the second question, one should note that we are not calculating an absolute displacement of a single point. We are rather calculating relative distances between two points. These points are affected equally by the camera movement.

Before closing this section, it is important to highlight that by visually inspecting all rockets launched from the southwestern site, we see that none of the earlier rockets seems to be traveling at a speed that is lower than the last rocket. In fact, we repeated the same procedure for a few other rockets just to confirm. We found the speeds were very comparable to the one quoted above for the last rocket.

Also, we see no visual evidence that any of the rockets launched at a very steep launch angle close to 90° (which shortens the range by a significant margin, making hitting the hospital a real possibility).

Horizontal distance traveled

Ignoring the deceleration caused by air resistance, one can easily compute the horizontal distance traveled by the last rocket from the time it was launched to the time of the explosion.

The transversal speed of the first rocket as calculated above is 703.28 m/s. Using this speed, one can resort to the cosine definition to compute the horizontal speed. We find it to be 561.66 m/s (561.66 m/s).

The horizontal distance traveled during the 5.13 s of the flight is 1916.7 m, as shown above. Since the time between the first rocket launch and the explosion is 30.3 s we can now compute the horizontal distance traveled (d₁+d₂ in Figure 2) as follows: 561.66 m/s x (30.3-5.13) s + 1916.7 = 16, 054 m.

The above calculation ignores air resistance. Using Equation 3, we can calculate the horizontal distance traveled, including air resistance. We will assume a Q-20 rocket was used.

The warhead weight of a Q-20 is 30 kg. We will assume the casing weight after fuel was consumed to be 10 kg.

There is no mention of the rocket’s diameter (which will allow us to calculate the cross-sectional area A). From the image shown here we estimate the diameter to be 16 cm (or 0.16 m). So A=\pi(\frac{0.16}{2})^2 = 0.02 m2. The air density \rho is equal to 1.2 kg/m3 at sea level and a temperature of 20° celsius. The air density is reduced at higher vertical distance. We can ignore the dependency on temperature as it doesn’t vary much for our ranges of temperature (say between 0° and 30° celsius).

As for the dependency on height, we will use an air density value of 1, which is more realistic given the heights we are dealing with (it is kind of an average of the heights. See this table). As for the drag coefficient c_d, we don’t know its exact value but it typically varies between 0.1 (for a well-designed rocket or bomb like MK-82) to 0.75 (for a model rocket). We expect the drag coefficient of a Hamas rocket to be in between these two extremes.

Using Equation 3 with the above parameter values, and assuming the drag coefficient c_d is 0.1 we find that the total horizontal distance traveled is 1916.7+12087= 14, 014 m (compared to 16, 054 m when no air resistance is present). When c_d is 0.75, the distance is 8, 806 m (compared to 16, 054 m when air resistance is not present).

We also ran computer simulations, and the results we obtained are close to the numbers obtained above. We obtained 13, 736 m and 8, 350 m, respectively.

So, in the worst case scenario (i.e. when the drag coefficient is equal to 0.75), the rocket would have traveled more than 3.3 km past the hospital.

In the worst case scenario (i.e. when the drag coefficient is equal to 0.75) the rocket would have traveled more than 3.3 km past the hospital.

The likely horizontal distance traveled by the Q-20 rocket is somewhere in between those two extremes, as it is reasonable to assume its aerodynamics is a no-match when compared to the MK-82 bomb but is probably better than the model rocket one.

Rocket fuel

Unlike long-range guided ballistic missiles, short-range rockets contain enough propellant fuel that is only meant to cause a brief combustion reaction. This reaction that releases a massive amount of gas exerts a high enough upward pressure (i.e. a thrust) to put the rocket in the parabolic path we presented earlier.

Typically, this phase lasts for a few seconds, at the end of which little or no fuel remains in the rocket fuel cylinder. In other words, once the fuel is consumed, the missile moves in a free motion following a parabolic path (or close to the parabolic path once we factor in air resistance).

This explains why the Bat Yam and the Netivot video footage both show fireballs at the tail of the rockets lasting only for a few seconds (right after launch).

This leads us to the following finding:

It is unlikely that an errant Hamas rocket would have contained any fuel by the time it reached the hospital 5 Km away. 

It is unlikely that an errant Hamas rocket would have contained any fuel by the time it reached the hospital 5 Km away. 

Rocket failures

The three main rocket failures that can take place are related to incomplete combustion (mostly related to not enough fuel, or related to an unbalanced mix of sugar and potassium nitrate), manufacturing defects in the fins which typically cause stability issues, or disintegration of the entire body and/or head of the rocket due to poor assembly/welding.

The first type of failure typically manifests itself immediately after launch, while the second and third failures could happen early or later during the flight. 

The video below shows a Hamas rocket veering off its initial straight upward path. It seems the combustion during the boost phase is incomplete and this, in turn, causes the rocket to succumb to the downward gravitational force earlier in its journey. Also, the swirling motion points to a potential defect in at least one of the fins.

Video # 8 A misfired Hamas rocket.

What’s interesting to note is that it only took less than 10 seconds for the rocket to reach its unintended target. We don’t know what the horizontal distance traveled by the rocket is, but it is much more than a few street blocks (as seen in the video). Also, the smoke arising from the blast appears to be insignificant, which is consistent with the type of damage a Hamas rocket typically causes.

It should be stated that by examining the Netivot video footage, we find no visual evidence that any of the rockets launched from the southwest location exhibits a similar errant behavior.

It should be stated that by examining the Netivot video footage we find no visual evidence that any of the rockets launched from the southwest location exhibits a similar errant behavior.

It is also clear none of the rockets launched from the southwestern location (when viewed from the Netivot footage) took a sharp upward trajectory. A sharp upward launch angle of 80°, for example, would shorten the horizontal distance by a huge margin, making it possible for the rocket to fall in the courtyard of the hospital (revisit Equation 2).

Also noteworthy to mention is that none of the prior rockets traveled at a significantly slower average speed than 467.56 m/s (the average speed of the last rocket). This is evident by the fact that none of the rockets caught up with any other rocket launched before it. 

Having said that, the last rocket, or one of the earlier rockets, could have disintegrated along its journey. If that is the case, the failed rocket could not be the one that hit the hospital.

The reason is that, as we will see later, the object that hit the hospital had a “healthy” sound signature, one that is consistent with a bomb or a missile with a whole casing cylinder and associated fins.

Damage caused by Hamas rockets

It is a fact that Hamas rockets don’t, in general, cause as much damage as traditional ballistic missiles. This is certainly the case for the Q-20 rocket which, has a small explosive payload.

In May 2021, Hamas fired 4360 rockets and mortar shells killing 13 Israelis. In another article, the IDF claimed 300 of those rockets landed in Gaza.

The IDF claims the success rate of the Iron Dome system is close to 90%. If we take this success ratio at face value then only (4360–300) * 0.1 = 406 exploded on the ground, claiming the lives of 13 Israelis (as reported in the above article). So on average, each rocket caused 0.03 deaths.

The 300 rockets that landed in Gaza killed 17 people. This means that, on average, each rocket caused 0.05 deaths.

This death rate is higher than the one on the Israeli side. This could be explained by the fact that Israelis take shelter after hearing the sirens. Also, the population density in Gaza is higher than that of any Israeli town.

What is notable here is that both ratios are very low, and this reinforces the idea that Hamas rockets don’t cause much damage.

Below are a few selected images from Sderot taken on October 17, 2023, on the same night the Al-Ahli Hospital attack took place. It shows the damage caused by the Hamas rockets, the same flying rockets we see in the Netivot video clip introduced earlier (i.e. Video # 4).

As noted above, one can’t resort to the argument that the fuel in the rocket exacerbated the damage caused by the rocket. We demonstrated that the fuel would have evaporated in the first few seconds after launch. In other words, the damage shown in the images below is the extent of damage that we should have seen in the hospital courtyard, and nothing more.

Image # 3: Damage caused by Hamas rockets that hit Sderot on October 17.

We stated above that the most conservative death estimate at Al-Ahli Hospital was 100 people (according to US intelligence). The highest estimate was 475 people (as reported by the Gaza health ministry).

Al-Jazeera reported that thousands of Gazans sought refuge in the courtyard of the hospital during the night of the attack.

The fatality ratio caused by commonly used Israeli bombs is shown in the image below. It gives the ratio of “incapacitating injury” depending on the distance from the impact point.

The GBU-39 10% ratio within a 30 m distance seems to be in line with the death toll at the hospital, as the casualties that would result from this ratio would lie between the death toll extremes noted above.

Image # 5: Incapacitating inury ratio of various bombs possessed by the IDF.

So what hit the hospital?

We demonstrated above that it is unlikely a Hamas/Jihad rocket hit the Al-Ahli Hospital on the night of October 17, 2023.

So what is it that hit the hospital then? And how did it happen? Unfortunately, we have no access to the explosion site. Even if we did, the passage of time would erase all the physical traces available.

That said, is it possible to use audio and video techniques to point us in the right direction? The answer is yes, indeed.

Audio analysis

It is well known that a certain bomb or a missile has a unique sound signature. This sound signature may differ slightly from one bomb/missile to another. The slight change comes mainly from the acoustics environment surrounding the explosion site.

Audio sound signature is a technique used in speech recognition. For instance, if two people pronounce the word “hello”, a good sound recognition engine would be able to identify the word despite the slight changes between their captured sounds, i.e. even if they utter these words in two different acoustics environment.

Sound signatures can be obtained in many domains, such as in time, in frequency, or in cepstrum domains.

We went ahead and extracted the sound signature of the bomb that hit the hospital. We used audio from the video clip below (Video # 9). This smartphone clip was taken on the fourth floor of a building that is located 160 m southeast of the hospital.

Video # 9: A smartphone located 160 m southeast of the hospital captured the explosion at Al-Ahli Hospital.

The video clip below shows a Hamas rocket landing in Tel Aviv. We extracted the rocket’s sound from this clip.

Video # 10: A smarphone captures the moment a Hamas rocket hit Tel Aviv.

The video clip below shows a JDAM-MK-82 bomb being dropped in Afghanistan. We extracted the bomb’s sound segment.

Video # 11: A JDAM-MK-82 bomb being dropped in Afghanistan

We imported all three clips into Audacity, a free open-source audio editor. For each audio, we only kept the relevant sounds, including the pre-explosion whistling and the explosion itself.

We then conducted a spectrum (frequency) analysis to compare all three. The frequency signatures of all three are shown below.

Figure # 6: Frequency-based sound signatures (from left to right): Al-Ahli Hospital bomb/rocket, a JDAM-MK-82 , a Hamas rocket.

One can tell that the Al-Ahli rocket/bomb and the JDAM-MK-82 sound signatures resemble each other. For instance, for both, there is a sharp sudden decline of energy at high frequencies whereas the drop in frequency for the rocket one is gradual.

This is not surprising; simply listening to the three clips (using a headphone) the ear can attest that the bomb/rocket that hit Al-Ahli Hospital and the JDAM-MK-82 one are indeed similar.

Does this mean a JDAM-MK-82 bomb was used? Not necessarily. It could be a bomb that is aerodynamically similar to the JDAM-MK-82.

So according to the sound analysis presented above, it is unlikely the object that hit the hospital was a Hamas rocket.

According to the sound analysis presented above it is unlikely the object that hit the hospital was a Hamas rocket.

Why is the crater so small?

The crater the explosion caused was small compared to those caused by other bombs dropped by the IDF. 

The various 500-pound to 2000-pound bombs the Israeli air force dropped in Gaza caused meters-deep craters with diameters ranging from 5 to 30 meters.

The small diameter of the crater in the courtyard at Al-Ahli Hospital led the media to speculate the object that hit the courtyard could only have been a Hamas/Jihad rocket.

The various media investigations stopped short of exploring other weapons that could have been used.

The fact that Israel used an illumination shell (see video and image below) to cause minor damage in the hospital building three days before is an indication that Israel was rather trying to scare the hospital staff after the latter refused to evacuate the hospital.

Video # 12: The aftermath of the attack on Al-Ahli Hospital on October 14.
Image # 6: Illumination shell that targeted Al-Ahli Hospital on Oct 14.

It is very possible Israel was still giving weight to the world’s perception of its disproportionate use of force (as it was still early in its campaign- the gloves went off later).

The question is then: did Israel drop a small collateral damage bomb in the courtyard of the hospital (notice the hospital building was not the target as the purpose was mainly to scare the hospital staff) to send a stronger signal to the hospital staff to evacuate the building? It is indeed very plausible.

It is also possible the IDF was not aware many Gazans had gathered in the courtyard to seek protection (Hananya Naftali, a Netanyahu aid, only deleted the following tweet after it was revealed the civilian death toll was high).

Image # 7: A tweet by Hananya Naftali shortly after the blast took place.

So what type of bomb could Israel have used in this case given the small crater and no remnant of the bomb was to be found?

The clue might be found in what the Hamas spokesperson told the media the day after the incident took place. When asked to produce remnants of the weapon that hit the courtyard of the hospital, a Hamas spokesperson who was interviewed by the NYT said, “The missile has dissolved like salt in the water. It’s vaporized. Nothing is left”.

Could this claim be true? In other words, is there a bomb that can disintegrate after the explosion, leaving no shrapnel behind? The answer is a definite yes. 

Within the last few decades, there have been efforts by the US government to work on weapons that have a programmable lethality built into them. This is typically achieved in two ways: by using a carbon composite casing that disintegrates after the blast, and by programming the lethality ahead of releasing the bomb (on the fly programming).

The carbon composite casing not only limits the collateral damage to those present within the immediate vicinity of the explosion but also disintegrates after the explosion.

One such bomb is the BLU-129 one shown below.

Image # 8: BLU-129 bomb and its main feature.

The video below mentions more features of the BLU-129 bomb.

Video # 14: Features of the BLU-129 bomb.

Another candidate bomb is the GBU-39 bomb. It is a Small Diameter Bomb (SDB). There is a version of this bomb (GBU-39A/B, described as a Focused Lethality Munition) where the metal casing is replaced with a carbon fiber casing.

It is not known publicly whether Israel has any BLU-129 in its possession, but we do know Israel has a stockpile of GBU-39. It is possible part of this stock includes a GBU-39A/B.

A small-diameter Focused Lethality (FLB) bomb is shown below being dropped on a mock target.

Video # 15: FLM bomb being dropped on a mock site.

The following image shows the damage caused by the SDB-FLM bomb shown in the video above.

Image # 9: Damage caused by a small-diameter FLM bomb.

Note that the explosion was not activated by a proximity switch. The explosion happened on impact, and yet no huge crater was created.

What is also interesting to highlight in this mock test is that one of the cars was simply displaced while the other almost flipped, if it was not for the presence of the structure to the left.

This is consistent with the damage caused in the courtyard of the hospital, where one car was flipped (see image below) while others were simply displaced or sustained mild damage.

 Also, the structures in the mock site are still standing and only sustained superficial damage. This is again consistent with the hospital explosion aftermath, where the buildings surrounding the courtyard only sustained minor damage.

Image # 10: The courtyard of Al-Ahli Hospital on the morning of October 18.

Before closing this section, I want to mention that it is possible part of the bomb’s tail kit was preserved. The kit, especially the guided one, is made out of steel. We may not find out until the war is over and whether Hamas will deliver the goods.

Who threw the bomb?

This is the million-dollar question.

There are two main challenges to answering this question with absolute certainty:

1- No independent investigator had access to the blast site immediately after the incident. By now, the site is contaminated and is of no use to collect any credible piece of evidence.

2- There is no visual evidence as to where the bomb or the missile originated from.

The best evidence we have is this 5-minute video that was recorded the day after the incident. There is no apparent remnant of the bomb/missile, at least one that is visible in this video.

What is also striking to notice while watching the video is that no fragments can be found on the ground. Knowing that a rocket or a bomb typically leaves thousands of sharpnels with different shapes and sizes, it is almost impossible for the Hamas authorities to have collected these small pieces in under 24 hours.

Video # 16: Walk-through of the courtyard of Al-Ahli hospital on October 18, 2023.

So what remains is what we can glean from other video and audio evidence.

If you recall, there were two aircraft that approached the hospital from the northwest direction. Both flight paths are shown in the map below. Notice that the angle between the flight path and the green balcony camera (i.e. Video # 9) is 35°. This is the same angle where the missile/bomb could have come from according to this report.

Map # 3: The flight paths. The aircraft started retreating making a 120° left turn after dropping their loads.

The dotted lines show the extrapolated flight paths. What is interesting to note is the following: The hospital explosion and the two other explosions that took place before it lie on the same extended flight path line. This observation was also noted in this study.

The hospital explosion and the two other explosions that took place before it lie on the same extended flight path line.

Why is this significant? If a pilot has to drop more than one bomb, he has to approach the targets from an angle that will allow him to reach both sites without much maneuvering. This is especially true when the bombs that are about to be dropped are unguided (aka dumb bombs). Out of the tens of thousands of bombs Israel dropped on Gaza, close to 40-45% were dumb bombs.

So the angle of approach was not chosen randomly. It is planned ahead of time. This is an indication that one of the two aircraft dropped two bombs: one bomb on the hospital and another one towards the southeast of the hospital (most likely that was the later aircraft). The locations of first and second explosions are marked on the map above (orange circles in Map # 3). We use a circle as we couldn’t pinpoint their exact locations. So the explosion exact impact point lies within the circle.

It is not known what the other targets were but, it is possible the bombs targeted a mosque or two as many mosques are situated in that neighborhood. It has been reported that Israel destroyed more than 100 mosques in Gaza.

The sound of approaching and retreating aircraft

The Al-Jazeera cameraman Hamdan El-Dahdouh filmed the three explosions with his smartphone.

This took place around the same time the main broadcast Al-Jazeera camera was on air. It was filmed in the same location (see the red camera icon in Map # 3).

Video # 17: Video footage that captures the three explosions along with the sound of two approaching and retreating aircraft.

The first explosion is captured shortly after it took place, around the 4th-second of the video. Also, and at the same instant, the launch of the Iron Dome missile has just been initiated.

At the 14th-second, we hear the sound of an approaching aircraft. This is the sound of the earlier aircraft. We know this by synchronizing the sound of this clip with the Bat Yam video clip.

For proper synchronization, one has to account for the sound wave to travel from the aircraft to the microphone camera (the height is approximately 4445 m as we will demonstrate later). When we do that, we conclude the sound appearing at the 14th-second is that of the earlier aircraft.

At the 20th-second, we see the midair explosion caused by the Iron Dome interception of a Hamas rocket. We also hear the sound of a drone.

At the 25th-second, we see the second explosion. 

At the 27th-second, we see the third explosion (the Al-Ahli Hospital one).

At the 38th-second, we hear the sound of an approaching aircraft. This is the sound of the later aircraft.

We repeat here the same synchronization procedure we did for the earlier aircraft. When we do that, we find that the sound appearing at the 38th-second is when the later aircraft is closest to the camera.

The above clip allows us to extract the various distances. The distance is easily found by calculating the time difference between when the fireball appears and when the microphone picks up the sound. We then multiply this time difference by the speed of sound (which is 343 m/s at 20° Celsius).

It should be noted that the speed of sound increases with temperature. It doubles around 1000 °C. So for a sub-100ms duration, while the heat from the explosion is still high, the sound wave will travel at a higher speed. This means the distance found with this method gives a tight lower bound on the distance (i.e. the actual distance is a tiny bit longer).

Distances:

1- Smartphone camera to the first explosion site:

It took 9.233 seconds for the sound to reach the smartphone microphone. So the distance is 9.233 s x 343 m/s = 3166.92 m

2- Smartphone camera to the second explosion site:

It took 9.7 seconds for the sound to reach the smartphone microphone.

So the distance is 9.7 s x 343 m/s = 3327.1 m

3- Smartphone camera to the third explosion site (the hospital one):

It took 4.237 seconds for the sound to reach the smartphone microphone. So the distance is 4.237 s x 343 m/s= 1453.29 m.

These estimated distances coincide well with the distances found through tringulation in Map # 1.

Decoy flares

Observing the later aircraft from the time it was approaching the shores until it made a 120° left turn, we notice it releases multiple decoy flares.

These flares are used to mislead any heat-seeking ground-to-air missiles. They are typically used just before or just after releasing a bomb, or when the pilot feels there is a real threat.

The video below shows an IDF aircraft carrying out a bombing mission in the vicinity of the Al-Quds hospital. A male background voice is heard saying “It’s gonna strike again” right after the aircraft releases a decoy flare. It seems that whoever said so may have most likely witnessed other instances of aircraft bombing other sites (a few thousand bombs were dropped on Gaza in the first two weeks following the October 7 attacks).

Video # 18: Attack on the vicinity of Al-Quds Hospital showing the decoy flares being released by an aircraft.

Speed of the aircraft

We now focus our attention on the two aircraft. We need to find the speed these aircraft were traveling at. We also need to find the altitude. 

Once we estimate these quantities, we can then resort to a few kinematic equations to allow us to find the time a bomb would take to reach the ground. We can also find the horizontal distance traveled by the bomb.

We use the Bat Yam footage for this purpose. This footage allows a side view as the planes move inward toward the city. 

We can estimate the speed by first estimating the distance the aircraft traveled inland, i.e. from the shore until the time it made a 120° left turn (towards the northwest of Gaza city). We use the later aircraft for that purpose.

We know from Google Maps that the distance from the shore to the hospital is 3.5 Km (along the flight path). Using the same ruler method described earlier, we find that the later aircraft traveled 5 cm (in the camera view plane) before retreating. It took the aircraft 18 seconds to travel this distance. The remaining distance to the hospital is 0.5 cm. So the actual distance traveled is 4.5 cm / 5 cm x 3500 m= 3150 m.

Therefore, the estimated average speed of the aircraft is 175 m/s (which translates to 630 Km/h). It is possible the aircraft deviated from this average speed, by speeding up or slowing down, along its path.

We can reuse the same inland distance to estimate the height. In this case, we have to account for the projection of the viewing angle plane. We estimate the angle between the viewing angle plane and the flight path to be 30° (we do that using Google Maps). Using the cosine definition, the 3.5 Km distance new reference is 5 cm x cos(30°) = 4.33 cm.

So every 4.33 cm in height corresponds to 3.5 Km. We measure the height from the ground to the aircraft. We find it to be 5.5 cm. So the height is 5.5 cm / 4.33 cm x 3500 m = 4, 445.72 m.

To summarize, the later craft was traveling at an average cruising speed of 175 m/s and an approximate cruising altitude of 4,445.72 m.

The plausibility of the aircraft dropping a bomb before retreating

We are going to focus on the later aircraft, as we suspect this aircraft was behind the hospital explosion (because of the timing correlation).

The time for the bomb to reach the ground, in the absence of air resistence, is unrelated to the velocity of the aircraft (assuming a horizontal flight path). It is proportional to the height and can be calculated using the following equation:

t= \sqrt{\frac{2h}{g}} \hspace{120pt} (6)

h is the height of the flight and g= 9.81 m/s² is the downward gravitational acceleration. This equation assumes air resistance is equal to zero.

Using the above equation we find that the time for the bomb to reach the ground is 30.12 seconds at a 4445.72 m height. 

If we include a quadratic drag force, we need to resort to computer simulations as there is no closed-form solution. The following equation is a good approximation:

t= \tau \text{cosh}^{-1} \exp(\frac{h}{\tau v_{t}}) \hspace{100pt} (7)

\tau= \sqrt{\frac{2m}{\rho c_d A g}} \hspace{175pt} (8)

v_t= \sqrt{\frac{2mg}{\rho c_d A}} \hspace{185pt} (9)

c_{d} is the drag coefficient, \rho kg/m3 the air density, A m2 is the cross-sectional area of the bomb and m kg is the mass of the bomb.

If we assume a GBU-39 bomb was used, we have m=129 kg and A= \pi (0.19/2)^2= 0.028 m 2. Assuming \rho=1 and c_d=0.1, we have t=30.34 seconds. If we assume a drag coefficient of 0.5, we have t=31.33 seconds. In both low and high drag cases, we notice that the time to impact differs only slightly from the ideal one.

Assuming air resistance is zero, the horizontal distance traveled by the bomb is 175 m/s x 30.12 s = 5271 m. Resorting to Equation 3 we compute the horizontal distance to be 5162 m (for c_d=0.1 ) and 4799 m (for c_d=0.5 ).

We ran computer simulations to confirm the accuracy of the numbers obtained above. We obtain 5148 m and 4748 m, respectively. Fall durations are 30.50 seconds and 31.97 seconds (see Figure # 7 below).

Figure # 7: Horizontal distances traveled by the bomb for different values of the drag coefficient.

It should be noted those distances are the maximum that can be achieved using guided or unguided bombs. Guided bombs, as explained in the following sections, has the ability to stear its fins to influence the horizontal distance (up to the maxium that can be achieved) where’s the unguided one doesn’t have this advantage.

Remember, we are not trying to make precise calculations for targeting a site (in which case we have to be precise down to a few meters precision). We are simply trying to find out the plausibility of this aircraft being behind the hospital attack.

If we examine where the aircraft was located 31.97 seconds and 30.50 seconds before the hospital explosion, we find it was 5.4 / 5 * 3500 m = 3780 m and 5.8 / 5 * 3500 = 4060 m, respectively.

Those two distances (3780 m and 4060 m) are below the maximum achievable (4883 m and 5184 m). In other words, the hospital is located within a striking distance from the aircraft. Therefore, we conclude that it is very plausible the later aircraft was behind throwing the bomb on Al-Ahli Hospital.

One important question to ask here is whether the 2nd explosion (the one that took place 2 seconds before the hospital one) was also caused by the same aircraft.

The 2nd explosion site was approximately located 1.3 Km northeast of the hospital. Assuming the bomb that hit the 2nd site was released at the same time as the one that hit the hospital, the distance would be 5080 m (3780 m + 1300 m) on the lower end and 5360 m (4060 m + 1300 m) on the higher end.

These two distances slightly exceed the reachable distances shown in Figure 7. It is possible we underestimated the aircraft speed. In other words, there could be a mismatch between the instantaneous speed just before the bomb was released and the average speed we used in our calculation. So it is possible the instantaneous speed was higher (i.e. the aircraft was accelerating gradually as it was heading inland).

A computer simulation shows that a release speed of 200 m/s (with a drag coefficient of 0.5) would achieve the maximum distance of 5360 m required in this case.

A question that legitimately arises is how could an explosion that is farther by 1.3 Km explodes first (approximately 1.63 seconds before). There are two possible explanations for that:

1- The bomb was released shortly before the hospital one.

2- The bomb was released at the same time but has a lower drag force than the hospital one. In other words, the bomb is not similar. According to this study, the MK-82 bomb has a very low drag force that ranges between 0.1 to 0.32 depending on the configuration. Also, a heavier bomb travels farther horizontal distance while taking less time. The Ashdod footage (Video # 3) clearly shows that the glare generated by the explosion of this bomb is easily noticeable while the hospital one was barely visible. This reinforces the idea this bomb is more powerful, i.e. heavier than the hospital one.

The temporal and spatial correlation between where the plane was, when/where the hospital explosion happened and when/where the other explosion took place (only 1.63 seconds before the hospital one) leaves no doubt the later IDF aircraft is behind the attack.

Guided vs unguided bombs

One other important aspect to mention here is the use of guided vs unguided [dumb] bombs.

A guided JDAM bomb was very likely used as to be able to control the horizontal distance (constrained by the maximum achievable) traveled by the bomb (the fall time will still be almost the same as the vertical movement is almost independent of the horizontal one, especially for small values of the drag coefficient).

Guided bombs have a circular error as high as 5 m while unguided ones have a circular error of up to 30 m.

Regardless, a pilot on such a bombing mission will drop the bomb as if it were unguided, since the bomb has no built-in propulsion engine.

The guided bomb will use its built-in GPS (i.e. the JDAM system) to steer the fins in a way to get the bomb to its intended target with more accuracy and precision.

The ongoing correction, based on a continuous feedback loop, kicks in right after the bomb is released from the aircraft. The higher the altitude of the aircraft the better as it will give the GPS guidance system more time to readjust.

Conclusion

Let’s agree on one thing: the two IDF aircraft were not simply having a picnic around the time the explosion at Al-Ahli Hospital took place.

The various media outlets that investigated the Al-Ahli Hospital explosion either ignored their presence [all investigations except the Le Monde] or downplayed the significance of their presence [Le Monde investigation].

In this comprehensive investigation, we demonstrated mathematically that it is unlikely a Hamas/Jihad rocket hit the hospital. Rather, it is very likely that a small-diameter low-collateral-damage aerial bomb was dropped from one of the two aircraft (most likely the earlier one).

In summary, here’s why we believe the IDF is behind this war crime:

Historical and contexual evidence

  • Israel has targeted medical facilities and ambulances in previous conflicts (not to mention the ones targeted since October 7).
  • Israel has warned the hospital staff to evacuate in the days leading up to the incident.
  • Israel has an established record of denying committing a crime only to admit committing it years later, after revelations of mounting incriminating evidence (e.g. the assassination of Al-Jazeera journalist Shireen Abu Akleh).
  • Israel attacked the hospital with an illumination shell 3 days before.
  • Hananya Naftali, a Netanyahu aid, tweeted about targeting a hospital an hour after the blast. He later deleted the tweet the next day after the death toll was announced.
  • Biden refused any international investigation into the matter.

Summary of our investigation

  • A Hamas rocket could not contain any remaining fuel by the time it reached the hospital (fuel burns within a few seconds after launch). Therefore, its destructive capability is very limited and would certainly not cause the death of 100 people or more.
  • A disintegrated Hamas rocket could not have hit the hospital because the sound whistling generated by whatever weapon that hit the hospital was whole, i.e. a missle/bomb with a full body including the fins.
  • The frequency-based sound signature of the weapon that hit the hospital resembles that of an aerial bomb (most likely equipped with a guidance system such as the JDAM) rather than that of a Hamas rocket.
  • We demonstrated mathematically that the hospital was within a bomb-dropping striking distance from one of the aircraft that was flying over the vicinity of the hospital.
  • The sites of the two explosions that preceded the hospital one were on the same extended flight path. This is a typical bombing mission tactic when an aircraft is assigned to hit more than one target.
  • Based on a 3D Doppler shift analysis study, referenced earlier, the weapon that hit the hospital most likely originated from an angle that is 35° from the southwest when compared to the balcony camera view axis. According to our triangulation, this coincides well with where the two aircraft were approaching the hospital from (the southwest rocket launch site was located at 85° when compared to the balcony camera view axis).
  • It is very likely that a small diameter bomb like the GBU-39A/B was used. This bomb has a carbon fiber casing, which leaves no trace behind as the body disintegrates immediately after impact. This bomb, also dubbed as a Focused Lethality Munition (FLM) bomb doesn’t cause a huge crater after impact.

Before closing, let me say this investigation took over 400 hours of work spread over the past three months. It was made possible by the availability of open-source information and knowledge.

If you have a comment or a critique to make, feel free to write it in the comments section below.

I have the intention to keep adding more material as further supporting or contradicting evidence becomes available.

Stay tuned!

Appendix

The following two video clips were presented as evidence in some of the investigations.

It should be noted that the first clip doesn’t capture the Al-Ahli Hospital explosion or the two explosions that preceded it. It is evident from the timestamp it was recorded one hour after the Al-Ahli Hospital explosion took place. We do see an IDF aircraft retreating after dropping its load.

There is no timestamp in the second one, but we know it doesn’t capture the Al-Ahli Hospital explosion. However, it does capture the first explosion. We chose not to use it in our investigation as the salvo of rockets we see are fired from two different locations. As such, we can’t isolate the ones that were fired from the southwest location.

Video footage recorded by a smartphone located in Netivot. The footage captures an explosion that took place one hour after Al-Ahli hospital one. We clearly see an IDF aircraft retreating after dropping its load.
Video footage recorded by a CTTV located in Netiv HaAssara just across the northern border of Gaza.

One response to “How The Media Misled The Public About Who Was Behind The Attack On Al-Ahli Hospital”

  1. […] Maher Arar has written a fascinating blog, “How the Media Misled the Public About Who Was Behind the Attack on Al-Ahli Hospital”. From an engineering and a technical perspective, Arar analyses who did bomb the Gaza hospital in October 2023. Many will remember the War on Terror in the wake of 9-11. He was jailed in a Syrian prison cell that he called a “grave” for a year. And it was the RCMP and the Canadian government which were at fault for fingering him to the CIA as a possible terrorist — of course he was nothing of the sort. You can read this impressive article here. […]

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