Can Physics Prove If We're Being Lied to About the Downed Russian Jet?

On Nov. 27, Tom van Doorsslaere and Giovanni Lapenta, Belgian astrophysicists at KU Leuven, wrote a blog post analyzing the physics of the Russian fighter jet that was shot down by the Turkish military on Nov. 24. Motherboard ran a write-up of the physicists' account the same day, and since then we've received plenty of feedback about just how full of errors their analysis was. Apparently, van Doorsslaere and Lapenta were also on the receiving end of a barrage of criticism from a small army of "so-called experts," and felt the need to address many of these criticisms in a response to the original blog post.

"I have had quite a few critical thoughts on the Dutch version of the article," van Doorsslaere told Motherboard in an email. "They all come down to (so-called) experts claiming that you cannot treat a plane as a falling rock. They are quite right. The disappointing thing is that these experts never make any calculations themselves: they just point out we're wrong, without computing how their criticism will change our result."

So in keeping with the spirit of van Doorsslaere and Lapenta, Motherboard has decided to reopen the case of the downed Russian fighter jet, to see if physics really can help separate fact from fiction.

For starters it's necessary to determine what exactly were van Doorsslaere and Lapenta claiming in their blog post. In general they were making the argument that both the Russian and Turkish accounts of the incident were bogus, a conclusion they arrived at by applying basic principles of Newtonian mechanics to both the Turkish and Russian official accounts of the encounter.

According to the due, from a video of the plane crashing (shown below), it is possible to approximately determine the altitude (4,500 meters) and speed (980 kph) of the plane at the time it was intercepted by a Turkish fighter jet. What does this tell us? Well, according to van Doorsslaere and Lapenta, it means either:

a) The Turkish military was lying about how many times they warned the Russian fighter jets about entering Turkish airspace: The Russian jets were in Turkish airspace for just 17 seconds, although the Turkish military said they issued 10 warnings over the course of 5 minutes before shooting down the plane. Traveling at a speed of 980kph, this means the jets would have been about 80km away from the Turkish border when they received the first warning. This is more than enough time for the Russian fighter jet to switch course and avoid entering the Turkish airspace, so it seems weird for the Turkish military to begin issuing warnings that far out, however the United States military confirmed that 10 warnings were issued.

b) The Turkish military was lying about how long the Russian fighter jet was in Turkish airspace: according to maps released by Turkey, the Russian jet was intercepted after traveling 2km in Turkish airspace. Yet if it was traveling at 980kph when it entered the airspace, then this distance would have been covered in 7 seconds, not 17. To cover 2km in 17 seconds, the plane would have had to have been traveling at 420kph. Yet based on the video, this could not be possible if the crash site was accurate (which according to Turkish reports, was 8km away from the place where the jet was intercepted).

c) The Turkish military is lying about how far the jet traveled after it was hit: if the plane was traveling slower than calculated, it would not have made it 8 km after being hit.

Many pointed to the oversimplified nature of van Doorsslaere and Lapenta's calculations, claiming that like typical astrophysicists, they treated the jet as a perfect sphere in a vacuum in their calculations leaving important aerodynamic forces out of the equation, such as lift and drag. In particular, many critics took issue with the physicists' statement that "because the vertical movement is only dependent on gravity (g=9.81m/s², z=gt²/2), we can calculate that the plane was moving at a height of at least 4500 meters [and] number is consistent with the Turkish statement of the jets being at an altitude of 19,000 feet (5800 meters)."

The issue at hand here is that the jet was subject to other forces besides besides gravity, like lift. Thus, if lift wasn't taken into account there is no way the physicists' calculations could be correct.

"Obviously an airplane generates lift force even after it was shot," van Doorsslaere wrote in his response. "The lifting force reduces the effective force of gravity, and thus the height at which the aircraft flew could be much lower. On the other hand, the altitude in both Turkish and Russian version is about 6 km: so it seems to be a reasonable assumption that this also was true."

Yet this raises another question—how long was the plane in the air after it was hit? In the video above, the plane takes about 30 seconds to hit the ground. The problem is, the video clearly starts after the plane was already hit. How long was it flying before the cameras started rolling? Ten seconds? Twenty seconds?

The amount of time it took the plane to fall from the moment it was hit until it crashed is a crucial variable in figuring out the altitude and speed of the jet at the moment of interception. If the plane was hit 10 seconds before the cameras started rolling, according to van Doorsslaere this would mean the plane was traveling at only 720 kph when it was hit (assuming that the distance it traveled post-impact—8 km—is accurate). Figuring out how long the jet was in the air is also complicated by the fact that the jet may still have been capable of thrust following interception, in which case it could have been accelerating at a rate faster than the rate of acceleration due to gravity.

There was also the claim that it's necessary to take into account the aerodynamic forces that will be slowing them down during their uncontrolled descent. Van Doorsslaere also acknowledges this, but notes that if the 8 km distance traveled after impact is correct, the result of friction acting on the falling aircraft (essentially slowing its horizontal progress) means that it must've been traveling significantly faster than 960 kph at the moment of impact. The downed Russian aircraft was a Sukhoi Su-24, which tops out at about 1,300 kph. Assuming it was going at its maximum speed when it was intercepted, this would mean that the craft was in Turkish airspace for less than 6 seconds.

There's also the possibility that the jet was going way slower than 980 kph. This was the opinion of one reader who wrote into Motherboard, claiming to be a retired Major General in the Turkish Air Force. According to him, in the video it is clear that the Russian jet is flying in "extended wing position," as it would when it was attacking a ground target. In extended wing position, the Major General explained, the Su-24 fighter jet would be flying much slower than 980 kph—probably closer to 550 kph, although he speculates that it was probably closer to 450 kph considering the jets were just coming off a bombing run.

Lastly, there's the issue with the Russian map, which shows the jet making a 90 degree turn after it was hit. As van Doorsslaere points out, while fighter jets can handle immense amounts of g-force, humans are not quite so sturdy. Although humans have survived upwards of 46 g, the typical amount of g-force experienced in a fighter jet turn is around 10 g—above this, it is not uncommon for humans to start blacking out.

According to van Doorsslaere, assuming that the Russian jet was traveling 960 kph when it was intercepted, this would mean that the radius of curvature would need to be around 700 meters or more for the pilot to experience 10 g. Yet on the map provided by the Russians, the pilot makes a sharp turn after being hit, the radius of curvature being on the order of just a few dozen meters, which would generate around 70 g.

The problem is not so much the amount of g-force experienced by the pilot (car crash victims have experienced over 100 g), but rather that such a turn would simply be impossible to bring about. According to van Doorsslaere, a damaged fighter jet could not generate the momentum to pull off such a turn.

So in the end, what is to be made of van Doorsslaere and Lapenta's account of the downed Russian jet? Well, while it is entirely possible that Turkey and/or Russia is lying about how the encounter went down, it is unlikely that we'll be able to solve what happened just based on the two countries' maps and a 30-second video depicting the last moments of the Russian fighter jet. At the moment, there are too many unknowns, such as how long the fighter jet was actually in Turkish air space and how long the jet was in the air after interception.

Without knowing the actual value of such variables, a more accurate take than van Doorsslaere and Lapenta's would be difficult since there is no way to know for sure how fast or how high the jet was flying. All we have is the Russian and Turkish accounts and a short video clip to go off, which were the source materials for van Doorsslaere and Lapenta's calculations.

That being said, if you think you can come up with a better mathematical solution for who is lying about the Russian jet, van Doorsslaere and Lapenta would love to hear from you.