The Reason High Temperatures Makes It Harder For An Aeroplane to Take Off

"Hello, we will have to delay the 11.45AM scheduled flight to 6 PM. The change is due to the excessively high temperatures (above 40 degree Celsius). Taking off in this condition is risky as the runway is not long enough to increase the lift required for such a journey with this temperature. We are sorry for the inconvenience and will throw in a complimentary meal during this waiting period. Thank you for choosing Flight Benus."

Mr Richard was infuriated as he listened to the voice over the airport's public address system. He planned to meet a friend by 2 PM, and this unscheduled delay had upset his plans.

Image from Pixhere

For him to understand why the high temperature is a problem for the aeroplane to take off, there is need to know how the aircraft flies.

How the planes fly: The Four Forces of Flight

Without a fundamental aeronautics knowledge, there is a chance you may have heard someone talk about "lift" which the plane's wings generate.

Well, that is just one of the forces that affect how an aeroplane flies.

To fly the following four forces come into effect:

1. The Weight: This is the weight of the aeroplane that acts in a downward direction, towards the centre of the earth. This is a force of the gravity.
2. Thrust: This is the forward propelling force which is found in the direction of aeroplane's travel. The plane's engine generates this forward force.
3. Drag: This is the force that acts in the opposite direction to the thrust. The friction and the difference in the air pressure creates drags
4. Lift: This is the force that acts perpendicular (right angle) to the direction of motion. It is produced similarly as the drag; due to differences in the air pressure.

Recall that force is the rate of change of momentum which is shown below.

From the Newton's Second Law of Motion, if mass (m) is constant, the sum of forces (F) which acts on an object is equal to the product of the mass (m) and the acceleration (a).

i.e.

F= ma

where

m= mass
a= accelareation

But acceleration is the rate of change of velocity.

Therefore we can rewrite the Second Law of Motion as

F= mass x rate of change of velocity = mv

If the mass (m) is constant

The rate of change of momentum = mv

Therefore

Force = rate of change of momentum

Now that we have established the relationship between the rate of change momentum and force let us consider the air molecules change of momentum as it collides with the aeroplane as it moves through the air.

The wings as it hits the air molecules change momentum which invariably means some form of force is at play.

Therefore the wings exert some magnitude of the force on the air which is similar to the magnitude of the force the air exerts on the wings.

Moving forward, recall that for every action there is an equal and opposite reaction- Newton's Third Law of Motion.

The force exerted on the wing provides the climb in the upward direction known as the lift, which exerts another force in the opposite direction (downwards) known as the aerodynamic drag or simply drag in accordance to the Newton's Third Law of Motion.

So these two forces always occur as a pair as there would no lift without a drag. The two acts on the plane, with the lift pushing it upwards and the drag pulling it towards the earth. The engine's thrust counteracts the drag to keep the plane from plummeting to earth.

The High-Temperature Problem

The equation of state has the relationship between pressure, density and temperature for a perfect gas.

p= RρT

p= pressure
ρ = density
T= absolute temperature (measured in Kelvin)

Looking at the equation which could be rewritten for density as

density (ρ ) = p/(RT)

The above equation shows the relationship between density and temperature to be inversely proportional. This relationship means an increase in density results in a decrease in temperature. Conversely, an increase in temperature results in a reduction of air's density.

The temperature of air measures the average speed of the moving air molecules. The air molecules are always in constant motion and collide with each other. Density is the mass of air molecules per unit volume. The higher the temperature, the more excited the collision of the air molecules and the more apart they become thereby increasing their volume.

Recall density
ρ= mass/volume

The increased volume means a reduced density.

That means the density of the air becomes "thinner" as the temperature increases.

This reduced density alters the lift-property of the air. The lesser number of molecules of air around the air wings would not be enough to generate adequate lift.

It also reduces the fuel/air ration required for combustion. The reduced density means a decreased molecules of air that will enter the cylinder for combustion to be more efficient.

But you can always compensate for the decreased air density if you could increase the speed of the aircraft. Here requires the longer runway which the, unfortunately, the airport in which the Bonus aeroplane is does not have. I guess Mr Richard will have to wait till 6 PM when the temperature is lower, or he can always use the road :)

REFERENCES

1. Relationship between Air Pressure, Density and Temperature
2. Aircraft Performance in Relation to Atmospheric Pressure, Density and Temperature
3. Newton's Laws of Motion
4. Why Phoenix's Airplanes Cannot Take Off In Extreme Heat