Push a Boeing 737 on ice: Did this guy have a chance?

Question

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

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.