In a 75 degree bank the cosine is 0.26 which means the airplane now needs almost four times as much lift. Pitching the airplane into such an attitude could well exceed the critical angle of attack and bring about wing stall -- which could be dangerous at such a steep bank angle.
Now it should be noted that all the above examples of airplane bank are assumed for a level turn, where the aircraft stays at the same altitude. This is the "standard" turn maneuver. If the airplane were to simultaneously bank and descend, there need not be any loss of lift (depending on bank angle and rate of descent), although the pilot must now be careful that the descending airplane does not overspeed, or enter a dangerous spiral dive.
Another technical point worth noting in turning maneuvers is that (in a level turn), the airplane (and pilot) weight increases due to centrifugal force, just as you may remember as a child on those spin rides, where you felt heavy and unable to move your arms or legs.
In a level turn the g loading is simply the inverse of our above bank-to-lift relation -- ie., g = 1 / cosine bank angle.
If the bank angle is 45 degrees the cosine is 0.7 and the g-loading is therefore 1 / 0.7 = 1.41. In other words, if the pilot weighs 100 pounds, she would now feel as if she weighed 141 lb. The aircraft's effective weight would be 1.41 times greater.
In a 60 degree turn g-loading is 2, so the plane and pilot's weight is effectively doubled. In a 75 degree turn the g-loading is 3.9, which means that 100 lb pilot would feel like she weighs 390 lb, and the airplane is nearly four times as heavy (at least as far as the unforgiving force of gravity is concerned). Again, this kind of steep bank angle would likely result in a wing stall.
Another important point to consider is altitude, which determines the air density. The higher the altitude, the lower the density (due to less air pushing down from above) and the higher the stall speed.
Let's first consider the "standard" published stall speed, Vs, which is typically given for landing and takeoff conditions at sea level standard day conditions, which means 15 C (59 F) and atmospheric pressure of 101.3 kilopascals or 29.92 inches of mercury.
At high altitude and thinner air, the stall speed can approach or even surpass the airplane cruise speed! A friend has flown hundreds of USAF missions in the Lockheed U2 reconnaissance airplane, considered the highest-flying jet in the world. The aircraft's cruise speed in that thin air at over 65,000 feet altitude is only several mph above its stall speed, requiring constant pilot attention to keep the aircraft in its very narrow safe operating speed range.
That is because the air molecules are so few and far between that the pilot must fly at a high angle of attack just to keep aloft. If he loses his concentration and the speed drops only slightly, the airplane wing will stall, and a recovery under those conditions might be very difficult.
In pilot circles this flight regime is known as the coffin corner. There have been a number of deadly crashes of high performance aircraft at high altitudes, prompting the FAA to issue an advisory on high altitude flight.
Now there is a mathematical formula that relates stall speed and air density:
Stall Speed = the square root of wing loading (which is the aircraft's weight divided by its wing surface area), times 2, divided by air density, and divided again by the wing's maximum lift coefficient. In mathematical terms the formula looks like this:
Vstall = sqrt( (W/S) * 2 / rho / CLmax)
Where W/S is the wing loading (or airplane Weight divided by wing Surface), rho is the air density and CLmax is the maximum lift coefficient.
So we can see just by looking at that relation that the lower the air density, the higher the stall speed will be.
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