Top Gun Maverick: Let’s do the Math(s)
I went to the cinema for the first time in years the other week to watch Top Gun: Maverick. It’s a bit of fun, not to be taken too seriously, and it’s essentially a repackaging of the plot of the original move with a few variations. For example, instead of a dogfight the climactic mission is to destroy the death star by flying down a long valley and dropping bombs into a ventilation shaft (although arguably it owes less to Star Wars than the British WW2 movie “633 Squadron”). The cast is a little more diverse but the rivalry and prevailing worldview remains the same — more on that here: https://medium.com/politically-speaking/the-first-15-minutes-of-top-gun-is-a-chronicle-of-americas-pathologies-23b114a6697
Military aviation is actually something I know quite a lot about. Of course, I could pick the film apart on many technical points like how radios and radar actually work, and the difference between radar-guided and infrared-homing missiles (you can’t decoy radar missiles with flares!), but as I have grown older and wiser I accept that you have to let lots of those things go. All the airborne action takes place with the aircraft ridiculously close to each other but it wouldn’t be anywhere near as visually appealing if the distances were true to life.
Overall, though, the flying sequences and the technical details are way better than the original Top Gun. One thing I noticed, though, is that this time round the movie is quite specific about numbers in terms of speeds, times and g-forces, so let’s have a look at how realistic they are.
Speed and Distance
The first thing we learn about the mission is that it will be flown at 660 knots.
The top speed of the F-18 is quoted in published sources as over 1000 knots, but it’s important to note that figure will be in a straight line, at altitude, and probably with a ‘clean’ jet without fuel tanks, bombs or targeting pods. External stores create drag and reduce the top speed, and at low level the air is denser so in practice 660knots might be difficult to achieve. You might even need to use afterburners to get to that speed so you would be burning fuel at a huge rate. On balance, 660 knots is fairly ambitious for low-level manoeuvring flight. Let’s go with it for the time being though.
At a critical point in the film, the top brass decide that the attack run should be flown in 4 minutes instead of 2 minutes 30. They’re concerned that the run as planned is not achievable and are implicitly prioritising mission success over the chances that the crews can survive, as it appears the extra minute and a half will allow the enemy’s 5th-generation fighters to intercept them. That’s the type of decision that might be made for a high-priority (probably wartime) mission, but the movie doesn’t really explore the implications.In practice, though, the longer run makes quite a difference. 660 knots works out at 11 nautical miles per minute, so a 2 minute 30 run would be 27.5 nautical miles. Flying a 27.5 nautical mile run in 4 minutes gives a datum speed of 412.5 knots. That’s about right for low-level manoeuvring flight, if a little on the slow side. I’d expect an aircraft like the F-18 to fly at about 480 knots at low level, perhaps 540 for an attack run (it’s good to have a datum speed divisible by 60 because that gives a round number of miles per minute, which makes the mental arithmetic for timing, fuel use etc much easier). 480 knots would give a run time of just under 3 minutes 30 seconds.
Why would you fly slower than your maximum speed though? Well, for a start it’s easier to manoeuvre and you don’t need to pull nearly as much g. A level 6g turn at 660 knots has a radius of 6500 feet (over a mile), whereas the radius of a 6g turn at 480 knots is about half that at 3500 feet, and 420 knots yields a radius of only 2600 feet. Or, to put it another way, to achieve a 6500 foot radius of turn needs a 6g turn at 660 knots but only 3.3g at 480 knots and 2.6g at 420 knots — much, much more comfortable and controllable. There may also be limits on things like weapon release — if you drop a bomb or fire a missile at too high a speed it can impact the aircraft as it falls away. I’m not an expert on the F-18 but I expect 660 knots would be pushing it!
Maverick decides to show the top brass and students that the mission as planned is feasible — in fact he decides to complete the run in 2 minutes 15 seconds instead of the 2 minutes 30 seconds. That’s quite a step up; it works out at a datum speed of 733 knots and you would need to pull 7.5g to achieve the same turn radius as the 6g turn at 660 knots. Also, for the critical 10g pull out of the valley, Maverick will now need to pull 12.5g — hence the jet no longer being airworthy at the end of the sortie as the g loading overstresses the structure. It’s also a recipe for g-induced loss of consciousness, depicted earlier in the film; sudden onset of high g is more likely to black you out than smooth and sustained application of g.
There’s another problem with this speed though. Let’s assume that when they are flying the practice runs in the California desert at sea level and with a temperature of around 30 degrees Celsius. The speed of sound at that altitude and temperature is 678 knots, so the 660knot run would be just below that. Maverick’s 2 minute 15 second run needs him to break the sound barrier. Worse, once the jets are in the “Rogue State”, the air is much denser. If we assume from the snow on the ground that the temperature there is minus 5 degrees Celsius, the speed of sound comes down to 634 knots, so we should expect sonic booms as the aircraft pass at 660 knots — that might alert the defenders!
And what about the Missiles?
That’s enough math(s) for now, but there are some definite questions to be asked about how missiles are used in Top Gun:Maverick, and a lot of these are about speed and time. We see two significant missile systems used in the climactic mission. The first are Tomahawk cruise missiles fired from a ship to disable the enemy airfield, and the second are the enemy’s radar-guided surface-to-air missiles.
The Tomahawk is a cruise missile intended to overwhelm enemy air defences by being fired in large salvos. They fly at ultra-low level to their targets at about 450 knots and deliver a 1000lb blast warhead. In the movie we see the salvo of Tomahawks flying high over the formation of F-18s at a significant overtake. They go on to crater runways and destroy hardened aircraft shelters on the enemy airfield. It’s an unusual choice of weapon as they’re not optimised for penetrating hardened targets such as runways or shelters. Their blast warhead would be much better employed against, say, enemy surface to air missiles or radars — which would have made the whole mission easier!
And about those surface-to-air missiles… they’re placed menacingly all the way along the valley but probably much too close to be able to engage the aircraft — generally missiles have a minimum range to allow them to arm themselves and manoeuvre towards the target after they come off the rail. What interests me most about these missiles though, is their speed profile. Like in many Hollywood movies, they come off the launcher really, really fast and catch up to the aircraft quickly. They then slow down to about the same speed as the aircraft for 10 seconds or so to allow for some evasive flying, then speed up again to come in for the kill. I probably don’t have to tell you that it’s not like that in real life!
The Verdict
Overall the movie seems to fetishise flying faster and pulling more g — that’s OK as far as it goes but I hope I have demonstrated that there’s more to it than that and that the figures are somewhat ambitious. I can’t say for sure that it isn’t feasible as presented but If I were planning the mission, I’d have done it very differently. There are holes in the technical background almost as big as in the plot, but it’s only a movie, and actually quite an entertaining one at that.
You can check some of my figures at the links below:
https://www.calculatoratoz.com/en/turn-radius-calculator/Calc-8532
