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In this video an airport worker (in blue) tries to prevent a Boeing 737 from sliding on ice in heavy winds:

enter image description here

Did he even have a chance?

On one side of the argument, the airplane is sliding due to the force of the wind being stronger than the force of friction against the ice. If the worker can counter that force to prevent it from rising above the static coefficient of friction with the ice, then he could prevent the plane from sliding further. Even if the wind could apply 1 Newton of force over the static coefficient of friction of the tires, the plane would slide. The worker should be able to apply a few tens of Newtons to counteract that a force of that magnitude.

On the other hand, how much force could he reasonably apply? Certainly no more than his own static friction with the ice would allow. Maybe the fact that he could dig heels into the ice would make his contribution significant?

Of course I don't expect the worker to stop the sliding plane, but could he reasonably have prevented the plane from sliding further?

dotancohen
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  • @MooingDuck: That is because I ask if the worker can prevent the plane from sliding further, i.e. when it stops between slides. In the beginning of the video, it can be seen that the plane slides a bit, then stops, before it starts to slide again. – dotancohen Aug 28 '15 at 10:07

3 Answers3

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Simple (Wrong) Analysis

Shoes

Assuming the coefficient of friction on the ice is approximately the same for the tires and shoes. It would do just as much good to get into the plane as to try to push it. Both would increase the frictional force by at most $\mu\,m\,g$ Having established an upper bound for the effectiveness of pushing we can compare this to the magnitudes of the forces already in place.

An empty 737 has a mass around 30,000 kg. A human on the larger side has a mass around 100 kg.

So the human pushing on the plane could increase it's resistance to sliding by about 0.3%.

Considering wind generally comes in gusts that vary by more than 0.3%, the plane would still slide during the gusts, though in theory slightly less than it otherwise would have slid.

Ice Cleats

Suppose ice cleats were available. Now the human's force to resist movement is not limited by friction but by strength. Unfortunately, the human squat record is for a force less than 6 KN. The coefficient of friction between rubber and ice is around 0.2 so the plane was already dealing with 60 KN of force. So in this case the human could increase the resistance to sliding by no more than 10%, this may be close to the variation in wind in non-extreme weather situations, and might have actually helped. However, it would have been extremely dangerous, and likely could have only helped for a very very limited time.

It it were me, I'd just shove the ice cleat under the tire and be done with it.

A more complicated Analysis

Having watched the video it appears that the aircraft is rotating rather than sliding sideways. This is important as it seems the rear tires are keeping traction and only the front tire is slipping. Thinking about the weight distribution of an aircraft, most of the weight is on the rear tires. In fact, for a 737 the front wheel weight seems to be around 15 KN, so using the 0.2 coefficient of friction that's only 3KN of friction. It seems that not only could a cleated (very strong) human help out, but could in fact push the plane back into place. Someone in just shoes could still help out to the tune of around 5-10% which could be significant. Note though it would be most effective to push near the nose as that would give the longest lever arm to give the most torque.

Community
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Rick
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    What about shoes with snow cleats on them? – Selene Routley Aug 27 '15 at 12:23
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    +1 for the "jam a cleat under the wheel," a sensible engineering solution. – Carl Witthoft Aug 27 '15 at 12:56
  • Terrific analysis, thank you! I'm happy to see that the little blue jacket man, had he been equipped and knowledgeable, actually stood a chance after all! – dotancohen Aug 27 '15 at 13:51
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    I'd just like to point out this is an Air Canada flight. And while we Canadians may not be as experienced as others in some areas, we know how to deal with cold weather. I guarantee you, that guy wasn't just sliding around on the ice. I wouldn't be surprised if he was the guy the airport hired to make sure planes didn't skid sideways across the ice. He definitely had snow cleats or something of the sort. – Jim Aug 27 '15 at 14:11
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    Note that, in addition to the plane rotating on the rear wheels, the front wheels are turned a bit to the right (there's a head-on view at 0:57 that shows it well), so in fact it's possible that it was rolling to some extent rather than just sliding. Perhaps if the pilot (were he in the cockpit) had straightened them out, that would have given our Hero in Blue more of an edge. – Reinstate Monica -- notmaynard Aug 27 '15 at 14:59
  • Hero in blue? Sounds to me like his name might actually be Clark Kent after all – Jim Aug 27 '15 at 15:07
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    @Jim that was a WestJet flight, not an Air Canada flight. (also a Canadian airline). If you look down in the comments, the man in blue was an engineer of some flavor. Cleats: Note that at one point, the engineer in blue did shove his foot next to the plane wheel... then thought better of it. – Yakk Aug 27 '15 at 15:33
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    Great question! Note - you guys are talking about cleats on the shoes. But note that: let us say the guy has no cleats at all: in that case, human feet (in ordinary boots) are incredibly good at finding small amounts of purchase on, for example, very small irregularities and cracks. In practice if you were trying to push something on that surface (in normal boots), you'd wiggle your sole through the trivial amount of snow/ice, and very likely find a small crack or irregularity on the concrete, which could give massive purchase. – Fattie Aug 27 '15 at 20:13
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    ... anyone who, say, builds robots knows humans are amazingly, astoundingly, good at applying forces as we're just so flexible and "intelligently movable". – Fattie Aug 27 '15 at 20:13
  • Your "more complicated" analysis turned out to be a lot simpler! – foobarbecue Aug 28 '15 at 17:15
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To add to Rick's answer:

Rick is right that it is only the front wheel that is skidding. Most of the weight is over the main wheels (it is essential that the centre of gravity be close to the main wheels, to ensure the plane does not pitch when the wheels strike the ground on landing.) Only a small amount of weight is on the nosewheel.

It would seem that what is causing the nose of the plane to rotate is a wind from left to right (see how the snow is falling) impinging on the tailfin.

For easy math, let's assume that the main wheels are exactly half way between the tailfin and the nosewheel, which is also where our hero is pushing, so the plane is acting as a lever with mechanical advantage 1:1.

Westjet uses 737-600/700/800's. According to http://www.b737.org.uk/techspecsdetailed.htm the tailfin area is 26.44m2 + 5.22m2 rudder, total about 30m2.

Assuming an air density of 1.3 and a wind velocity of 25m/s (90km/h, 56mph) we have a wind pressure of 1.3/2*25^2=406.25N over an area of 30m2, a force of 12.187kN.

Given that I picked these numbers as estimates, that's surprisingly close to Rick's number.

But to look at it another way, our hero is trying (with the help of the tyre friction) to stop the effect of high winds on a 30m2 surface.

He doesn't have a chance, unless you give him a pole several times longer than the plane to use as a lever.

Level River St
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  • Actually, the nosewheel does seem to be a bit further from the main gear than is the center of area of the vertical stabilizer. – dotancohen Aug 27 '15 at 16:36
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    Nice, we came at it from different directions and got within an order of magnitude. I think it's likely that guy could help in a small way, but couldn't come close to stopping the sliding. Oh, and I'd imagine the wind resistance from the fuselage and wings wouldn't be insignificant so the net torque is probably a bit lower helping bring our numbers closer. – Rick Aug 27 '15 at 17:48
  • @dotancohen Yes, planes with tricycle landing gear always have their main gear aft of their center of gravity. If they didn't, it would be easy for them to fall back onto their tail when on the ground, which is generally undesirable. Exact forward/aft location of center of gravity will vary with fuel load, cargo load, etc., but it's always kept ahead of the position of the mains (as well as ahead of the center of lift in order to maintain longitudinal static stability.) – reirab Aug 28 '15 at 18:09
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The person only needs to be able to counter the force acting on the plane to slow down the movement.

The force on the plane is from the wind - it'll be a reasonably big force because the plane presents a reasonably large surface area - but if the person is wearing ice spikes, it's not inconceivable that they could make a difference.

James Cane
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