Interesting. The distance of the stop has a lot to do with it, and this relates to G forces, which are what will kill you if nothing hits you, or you it. My friend crashed his C 150. He got it really wrong. I was one of the first there to pull him out. I measured the stopping distance, and figure it to be in the range of 12" from about 75 MPH, and the plane flipped. The propeller flange portion of the crankshaft was mostly peeled away from the crankshaft. The cabin doors still opened, and although the cabin was deformed, it held its shape well enough to not become a cocoon. We had no difficulty getting him onto the wing. The coroner told me later that his stopping force exceeded 200 G’s.
Does a 1400 pound C 150 hitting the ground at 75 MPH, and stopping in about a foot, math out to 200G’s?
Of the simple physics variables, I think speed, distance and sometimes mass will all play a part.
Taking deceleration to be the hazard, then a little physics (see below) suggests that Mass is irrelevant, for a given stopping distance.
Basically more speed is bad for you, and more stopping distance is good.
But if a more massive aircraft takes further to stop, which it might, then more mass is good.
One important caveat is that while average deceleration is useful as a ball-park number, peak decelerations can be more important, e.g, skidding over grass before hitting a tree/wall/building. In that case the relevant stopping distance is the crumple distance between you and the impact, not the total distance slid.
Taking Pilot DAR’s question as an example, and doing it in metric:
1400 lb = 636kg
75 MPH = 33.5 m/s
KE = .5 × 636 × 33.5 x 33.5 = 356,875 J
200 Gs = 200 × 9.81 = 1962 m/s^2
Force = Mass x Deceleration = 636 × 1962 N
1 ft = .3048 m
Energy = Force x Distance = 636 × 1962 × .3048 = 380,339 J
so the answer is yes, more or less, (I make it 188 Gs ;-)
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A little physics
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Kinetic_Energy = Mass x Speed_squared /2
Dissipated_Energy = Average_Stopping_Force x Distance
Average_Stopping_Force = Mass x Average_Deceleration
now, since the aircraft comes to rest, and energy is conserved, we can equate the two energies:
Mass x Average_Deceleration x Distance = Mass x Speed_squared /2
the Mass cancels:
Average_Deceleration x Distance = Speed_squared /2
solving for Average_Deceleration:
Average_Deceleration = Speed_squared / (2 x Distance)
I also calculated 190 G assuming constant deceleration. I believe the peak acceleration or blunt force may have been the critical issue in this case, not the average acceleration, although 190 G is a pretty high average. I understand this has to do with the frequency response of the body’s internal structures – and every crash is different in terms of G versus time.
The purpose of a harness (or a helmet with crushable liner) is to spread the deceleration over time, minimizing the peaks. Obviously a heavier vehicle will see lower decelerations when ploughing through obstacles, but if the cabin remains intact and the pilot is wearing a harness, the average acceleration of a vehicle stopping very abruptly is often survivable.
Energy is very abstract and hard to relate to, but down to earth when thinking in terms of height (which happens to be a form of specific energy, used in turbine technology, e = E/mg).
h = v²/2g
h = 33.5²/2g = 57.14 m
Stopping from 75 mph is the same as falling from 57 meters. 57 meters is what? a 30 stories building or something. Very few people survive such a fall. It is deadly even if you land in water.
David, that’s very educational, thanks! I was taught that chances of survival are inversely proportional to angle of arrival.
chances of survival are inversely proportional to angle of arrival
NTSB looked into this and survivability tails off above 45 degrees and over 60 knots. There is a Boeing table somewhere on the net, which shows % survival at speed when the cabin structure starts to break-up – from memory around 10% fatalities at 66 mph, over 75% fatalities at 110 mph+ The large aircraft typically impact (excluding CFIT) at below 10 degrees, but still tend to break up. There used to be a book with the cheery title ’Doesn’t matter where you sit’.
Mass may play an indirect role due to, typically, the lower stall speed?
The lighter fixed gear single engine aircraft do appear to have a lower fatality rate – below 1 fatal accident per 100,000 hours, compared to GA average of around 1.5 per 100,000. Whether this improved rate justifies reduced utility is debatable? or the reduced utility of the aircraft is a factor in the reduced rate (less exposure to severe weather, for example), combined with a higher likelihood that accidents will occur at slower, more survivable speeds.
Stopping from 75 mph is the same as falling from 57 meters. 57 meters is what? a 30 stories building or something. Very few people survive such a fall. It is deadly even if you land in water.
People can apparently withstand a quasi-static acceleration of about 50 G. PDAR quoted a stopping distance of about a foot from 75 mph, which would generate 190 G, but also said the aircraft turned over – which would reduce the deceleration to the occupants. If they themselves traveled four feet, the deceleration may be survivable. That’s what led me to guess that perhaps it was an even more sudden stop due to inadequate harness restraint that got the poor fellow. This kind of situation is in my mind when I tighten my five point harness before takeoff – the lesson to me of thinking this through in the past.
That’s what led me to guess that perhaps it was an even more sudden stop due to inadequate harness restraint that got the poor fellow.
Some cars (all cars?) tightens the seat belts automatically when the air bag goes off. In any case, 190 g is a lot. In terms of force that is 150 kN (if the person weighs 80kg). The thrust from the F-16 engine is 127 kN with full afterburner according to Wikipedia. So it is similar (a bit less) to being crushed against a wall by an F-16 at full afterburner.
So it’s like Petter Solberg said in an interview in British TV “It’s not the speed that kills you, it’s the smell” . P Solberg is famous for being a good driver and terrible in English. (“Smell” is a norwegian word for a load bang).
The car seatbelt pretensioners (some models only) have less to do with decelerating the occupant, and more to do with assuring that they are held firmly in the correct position in the car to get the greatest benefit from the airbag, and otherwise not bounce around in the cabin. Most motorists simply will not tolerate a seatbelt which is tight enough to actually do its job, so to get people to wear them, they are sloppy, but will tighten at the instant of the crash. A seatbelt, and in particular a shoulder harness, is vital in occupant safety during a crash. If your plane does not have a shoulder harness, have one installed. AC43-13 provides data to do it as minor modification, so not STC required, and the authority is hardly going to give an owner a hard time for using specified data for making a plane more safe!
