The Afghans who clung to the outside of the C-17 during takeoff probably had no clue how fast an airplane flies and thought it was like holding on to the outside of a bus or train. Within a few seconds of takeoff, the two people clinging on had to let go and fall to their death.
Assuming a normal size adult human male body, and average strength, and a good grip to hold on to, at what airspeed would the wind be blowing with such force that the person simply could not hold on anymore? (ignoring things like temperature or lack of oxygen)
I believe that would be totally dependent on individual hand/forearm strength and structure. That’s where the muscles that grip and their skeletal/connective tissue framework are located. Lower limit of about 1mph or less. Wide range of variables for determining an upper limit. I doubt that particular biomechanical formula has been derived.
Propose some values for ‘normal’ size and grip strength.
It’s not like there is a lot of stuff on the outside of an airplane to hang on to, the surface tends to be pretty smooth. That would make getting a good grip, and maintaining it, very difficult.
This is the sort of math stunt I like doing, but I haven’t got the time for it. I’ll give you some of the pieces, though.
What you’re interested in is the conversion of airspeed to drag force. That ties into the coefficient of drag calculations.
Cd = Fd/pV^2*0.5A
Where
Cd is the coefficient of dynamic drag (0.7 for a person in a skydiver’s head-down optimum position)
Fd is the drag force (in this case, 46 kg * 9.8 N/kg to overcome the young man’s grip)
A is the surface area of the man (which I’m not able to find at the moment, you may need to spitball that)
p is the density of the air, which you can assume is 101.3 kPa, standard atmospheric pressure (or just round it offf to 100 for this back of the napkin math)
and V is the airflow velocity, which you want to solve for.
That’s the strength with which you can squeeze something. We don’t have to squeeze the handle, here, just hold on to it. I guess that’d be called pull strength? Given that even a moderately fit person can hang indefinitely from a bar, it’s going to be at least the weight of a human.
To fully answer this, you’d first need to know the maximum weight a human can support while hanging onto a handle, and then you’d need the aerodynamic drag of a human as a function of speed, to find what speed corresponds to that force.
I suspect that the answer is going to come out to the same ballpark as human terminal velocity.
If you’re desperate enough and can jam your hands through the handles and rotate them 90 degrees you may be able to stay on until the velocity actually tears your hands off.
Tom Cruise did it. This is really him on the outside of the aircraft - no stunt double, no special effects. He did have a hidden harness. At some speed his legs are swept out from under him and I guess at that point the drag has surpassed his weight?
I’m going to point out that there are very much some grippable holes on the surface of that aircraft, which would make hanging on a LOT easier than with the normal, smooth, unbroken surface of the typical aircraft.
Recent personal research leads me to conclude that a reasonably fit young woman is capable of climbing about the underside of a B-17 at cruising speed.
I couldn’t do the work I wanted to do, so I came back to this problem.
Googling had uncovered my Cd of a skydiving (head down position) of a human to be 0.7. It also gives a highest velocity of 240-290 km/hr. I just went for the easier numbers, called it 80 m/s. We’re dealing with huge margins of error here anyway, we’re gonna need bigger napkins.
I assumed our figure has a mass of 70 kilos, (~150 lbs) just so I could assign some drag force. The skydiver in terminal velocity, thus not accelerating, has a drag force equal to his accelerating force due to gravity, or 686 newtons. Air pressure is going to get divided out so I’m ignoring it*.
So I get 0.7A = 686N/3200mysteryvariableI’mignoring, or a “top” surface area of roughly 0.075 square meters.
Plugging all that back into my garbage equation:
.7 = 451 (the grip strength)/V^2*.5*0.075
V(airspeed)=131 m/s, or ~470 km/hr. This is for a person in a head-down optimal position, which in practice they may not manage. They may lose their grip at a much lower speed.
* All calculations are back of the napkin, and only touch on some of the more complicated aspects of aerodynamic drag. This is first year physics at best.
Notes I should have added is that this calculation is only for steady flight. In practice, a plane will be accelerating (magnifying the force the person requires) and will be climbing on take off. So the practical airspeed a person could hold on for will be quite a bit lower than what I calculated.
You missed a factor of 2 somewhere in there. Given you’re considering the grip strength to be less than the weight of the person, the speed should be lower as well. You can just scale the squared velocity by the difference in force.
Slightly outside the bounds of GQ, but that’s probably not true. A lot of them had probably flown a fair few times, and all of them would have seen planes before; it wasn’t ignorance that killed them. Not their ignorance, anyway.
"The next problem was Cruise’s safety harness. Though it was keeping him alive, its constricting nature was preventing him from using his body to act.
“I feel like a puppet,” Eastwood recalls Cruise saying. “I won’t be able to sell the fear.”
The crew added slack to the line, meaning that if Cruise lost his grip on the side of the plane he actually would have fallen several feet before the harness saved him.
“[In the scene] his feet slip off the plane and he really is holding on for his life,” Eastwood said. The handles Cruise clutches are actually panels used to cut down on turbulence as paratroopers exit the military aircraft."
The aircraft was flying at 185 mph and Mr Cruise was still holding on with his grip. He did not drop back and use the safety harness. Plus it was a steep climb for a better scene. He did EIGHT TAKES of the scene. I think he deserves credit for solving the OP’s question, or at least providing a high bar for the rest of us.
I haven’t seen the footage alluded to in the OP, but it’s worth pointing out that when people try to cling to aircraft typically they try to lodge themselves in the wheel well of the plane. So it’s not about grip strength at all.
However, the bigger problems are dying of exposure and/or asphyxiation. BTW this seems to have happened in this case too: human remains were found in the wheel wells of the military plane that flew from Kabul.
From the reports I read the people recently killed in the wheel well of a departing airplane were killed by the landing gear machinery crushing/mangling them - the human remains have been described as “parts”, not intact bodies which you’d get if it was just thin air and cold that killed them.
