A meme about whether an airplane can take off on a treadmill has been going around social media lately, tearing friendships apart with its divisiveness, ruining families and sending the world further into chaos. But now itās time to put an end to the madness. Letās look at the science!

The question goes like this: āImagine a 747 sitting on a large conveyor belt, as long and as wide as a runway. The conveyor belt is designed to exactly match the speed of the wheels, but run in the opposite direction. Can the plane take off?ā

The answer is yes, the plane will take off, and the explanation why is very simple. Iāll use some free-body diagrams (without coordinate systems, sorry enginerds) to break it down. But before we go into that, let the lovable folks from Mythbusters walk you through why the plane will indeed take off:

Like the Mythbusters say in the clip, the biggest reason why people get the answer to this question wrong is that they naturally tend to assume the plane would act the same was as an automobileāa vehicle that we all know would remain stationary on a treadmill.

But a carās propulsion system works differently than a planeās. I described how a vehicle drives forward in my Crawl Ratios and Off-Road Gearing: Everything Youāve Ever Wanted To KnowĀ article, saying:

The reason why your car moves forward at all is because the ground is actually āpushingā the car forward by reacting to your wheelās force against the ground. ļ»æ

In other words, your car moves because of FRT (the āthrustā) in the diagram above, which is only there because itās a reaction to the force that your tire imparts against the road. This force, labeled FTR above, is just your our wheelās torque (which is the torque from the engine multiplied by your trans, transfer case, and differential ratios) divided by the tire radius.

But if the car is on a treadmill, the ground can easily move relative to the vehicle. As a result, the engine will not produce much torque, the car wonāt be able to impart much of a force to the ground (other than to overcome frictional losses of the treadmill), and thus, the ground wonāt be able to impart much of a force back onto the car. The car will remain stationary.

Indeed, vehicle dynamometers actually uses rollers that have brakes to increase the āgroundāsā resistance. By doing this, theyāre gradually increasing the amount of torque the engine has to make to keep the wheels rotating (thus, theyāre increasing FTR andĀ FRTāhence why you need straps to hold the cars in place). Without adding resistance to the wheels, dynos could not produce a torque curve.

Airplanes work differently, in that they donāt send torque through tires, so they donāt receive thrust from the groundās equal and opposite reaction to the tangential force of the powered wheels. Instead, they rely on a reaction from air.

Airplanes receive their thrust by accelerating a āworking fluidā to ridiculously high speeds. Hereās NASAās definition of thrust:

Thrust is a mechanical force which is generated through the reaction of accelerating a mass of gas, as explained by Newtonās third law of motionļ»æ.

The key word, there, is āreaction.ā Hereās a look at the forces acting on a stationary jet engine, which would normally be attached to a wing (ignoring gravity for now):

That thrust pushing the engine (and thus plane) forward is equal and opposite to the force associated with the accelerated fluid spewing from the back of the engine. And as NASA derives on its website, the latter is simply defined as the rate of change of the fluidās momentum with respect to time.

Put another way, itās the difference between the gasās exit mass flow rate times the exit velocity and the entry mass flow rate times the initial velocity.

The thrust moving the plane forward is simply the opposite of the rate of change of momentum of the gas shooting from the back of the jet engines.