Pulling G!

You need to generate twice the amount of lift to fly a level 60-degree angle of bank turn. This in turn increases the stall speed by approximately 41%.

But why?

Firstly, I should say, this is not a lesson on flying 60 degree turns. It is a look at the theory of the forces acting on the aircraft in the turn. If you are learning to fly you should always listen to your instructor regarding turning technique for your particular aeroplane.

Secondly, Newtonian mechanics can be a complex area to understand. Naturally this short article does not delve into the depth of the different frames of reference one can consider when describing the forces acting on an aircraft. Instead it focuses on the forces experienced from the perspective of the pilot.

Now, with that out of the way, let’s start by a looking at a little geometry to set the scene.

In straight and level flight lift directly opposes, and equals, weight and we neither ascend nor descend. But in a 60-degree angle of bank turn, the lift is now not directly opposing the weight so we need to generate more lift to remain in level flight.

If you draw a triangle to represent the lift forces generated in a 2G turn you can see that this will give a vertical component of 1, i.e. 1G to oppose the 1G of gravity pulling you down – if this vertical component was any other value we would descend or ascend.

You’ll also note that this gives a horizontal component of 1.73G (which is the square root of 3). For those of you who are mathematically inclined you can work that out using the Sin function, bank angle (60 degrees) and hypotenuse (2) as below (remember SOHCAHTOA from school).

And then punch that into your calculator and you get,

This 1.73, is the bit of the lift that is turning the aeroplane. Now again, thinking back to high school and Newton’s third law, we know that there must be forces acting opposite to these as well. But what are they?

Well as noted above:

• opposing the vertical component (1G) is gravity
• opposing the horizontal component (approx. 1.73G) is centrifugal force/reaction (from the perspective of the pilot)
• opposing the lift (2G) is the load factor/apparent weight, or G-Force

So, using basic trigonometry and Newton’s third law we can see how and why the g-force increases in the turn, but how do we generate these forces and what are the implications?

Well once we’ve rolled in to 60 degrees angle of bank, we pull back on the stick. This increases the lift to twice the amount previously generated (2G) by increasing the angle of attack, however, it also correspondingly increases the drag. So, in order to overcome that additional drag, we increase power as well.

So now to remain in level flight we’ve got a higher angle of attack at the same speed as before and we’re using more power.

Now, assuming we are in balance and are flying a well executed 60-degree angle of bank turn (not easy, it takes practice) we should feel twice as heavy, e.g. be experiencing 2G.

That is the load factor or ‘apparent weight’ acting opposite the lift.

Another thing to note is that the stall speed has now increased by the square root of 2 (approximately 1.41/41%) – but why has it increased and why the square root of 2?

Well, as mentioned above we’ve increased the angle-of-attack to generate more lift, therefore we are now flying closer to the critical angle of attack, which is the point at which the wing will stall (regardless of airspeed). The second thing to realise is that it’s not just you that feels twice as heavy, the aeroplane also ‘feels’ twice as heavy, and we’ve added more power to maintain that level banked turn to counter the increase in drag generated by the higher angle of attack.

So, we’re now flying at a higher angle of attack, closer to the critical angle when the wing will stall but still at the same airspeed. This means that we will reach the stall at a higher speed than in straight and level flight.

Another way to think about this is to think about what happens if we increase the weight of the aircraft by loading more fuel or if, for whatever reason, we decided to carry an elephant or two onboard. Our take off speed will be higher as we need to generate more lift than a lighter less loaded aircraft. This is exactly the same idea, the heavier the aircraft, the closer to the stall it flies at a given airspeed.

In a 60-degree angle of bank turn the aircraft ‘thinks’ its twice as heavy. Therefore, because stall speed increases in proportion to the square root of the load factor (2G), our stall speed increases by square root 2, or 41%. Hypothetically, if we tried to do a 4G turn (don’t do this, most training aircraft aren’t rated to do 4G turns), it would increase by the square root 4, which is 2, therefore our stall speed would double.

This is one of the reasons why many aeroplane are limited to 60-degree angle of bank turns, as doubling the stall speed from say 45 knots to 90 knots would put you in a very dangerous flight regime with no margin for error.

So, hopefully that explains a bit about the mathematics and physics behind 60-degree turns. It pays to be conscious of this when flying these types turns and to ensure you have plenty of speed including a healthy margin above your stall speed when executing them.

Safe flying!