Why does stall speed increase in a banked level turn?

Note: I’ve moved my blog!  You can find this post here.

One thing you’ll read as a student is that stall speed increases in a banked level turn.  But why?  Let’s start from the beginning.  

When you first learn about the airspeed indicator, you learn that VS0 is the stall speed in the “landing configuration” (with flaps fully extended and landing gear deployed) and VS1 is the stall speed in a “clean” configuration (with flaps and landing gear retracted).  These speeds are marked on the airspeed indicator and thus it is easy to think that the aircraft’s stall speeds never change.

An example airspeed indicator.  Source: Wikipedia

An example airspeed indicator. Source: Wikipedia

It might surprise a student to learn that an aircraft’s stall speed is not constant.  From Wikipedia (emphasis mine):

The actual stall speed will vary depending on the airplane’s weight, altitude, configuration, and vertical and lateral acceleration.

On an airspeed indicator, the bottom of the white arc indicates VS0 at maximum weight, while the bottom of the green arc indicates VS1 at maximum weight.

Stall speed varies with the weight of the aircraft.  Let’s try to intuit why this is the case.

Everything in flying comes back to angle of attack (AoA), the angle at which the wing meets the relative wind.  Recall this graph of AoA vs. Coefficient of Lift:

Angle of Attack vs. Coefficient of Lift

Angle of Attack vs. Coefficient of Lift.  Source: Wikipedia

As you can see, an increase in AoA will produce more lift–but at a certain angle a further increase in the AoA will no longer produce an increase in lift.  This angle is called the critical angle of attack and is shown at the apex of the above graph.  An airplane will stall when its wings exceed the critical AoA against the relative wind.  Note that while stall speed varies based on weight and other factors, the critical AoA at which a specific airfoil stalls is constant.  

Recall the lift equation:

L = lift
rho = air density
Cl = coefficient of lift
Aw = area of wings
V = velocity (true airspeed)

We can rearrange the lift equation to show the minimum velocity an airplane would have to fly to support a given weight.  Remember, in level flight lift is equal to weight.  So we can substitute the lift in the equation for weight.

W = weight

W = weight

Note that in level flight we can’t change the air density or wing area, so those values are constant.  Also, since we want to inspect the stalling speed, we set the coefficient of lift to its maximum possible value (i.e. the value of the coefficient of lift at the critical AoA).  Now the only other variable on the right side of the equation that can be modified is the weight (remember, lift = weight in level flight).  You can see that increasing the weight results in an increase in the minimum velocity required to support that weight.  Thus, stall speed increases with an increase in weight.

Now let’s return to the real question: why does stall speed increase in a banked level turn?

During a level turn you will experience g-force–I’ve already explained this in an earlier entry.  Your plane will behave as if it is heavier than it actually is when under the effects of above-normal g-force.  ”Behave as if it is heavier?” you say?  Well there you have it!  Stall speed increases in a banked level turn because the g-force on the plane increases the effective weight of the plane, and stall speed increases with weight.

Here are some further observations we can make from the rearranged lift equation:

  • Since the weight of the plane affects the stall speed, that is one reason why it is said that “an airplane can stall at any airspeed.”  A heavier aircraft will stall at a higher speed than a lighter one.  (It’s also said that an airplane can stall at any attitude, but that’s a discussion for another day.)
  • This is a reason to be cautious when making steep level turns at slow speeds–your stall speed will increase the steeper your turn.
  • As you gain altitude your stall speed will increase since at higher altitudes the air pressure decreases.  This is tricky–the true airspeed at which you stall will increase, but the indicated airspeed at which you stall will be the same regardless of air pressure.  This is because an airspeed indicator works by measuring ram air and is actually a pressure sensor and not a true speed sensor.  Since ram air is a function of both air pressure and velocity, we can combine velocity and air pressure to modify our above velocity equation to:
    Vindicated = indicated airspeedThe pressure term (rho) was merged with the velocity to create the indicated airspeed variable.

    Vindicated = indicated airspeed

    Thus, you see that the stall speed shown on the airspeed indicator will not change with a difference in pressure.  (Though indicated stall speed will change with a difference in weight.)

  • On hot days your stall speed will increase since hotter air has a lower air pressure than colder air.   But again, the indicated airspeed at which you stall remains the same regardless of air temperature.
  • As you fly and burn off fuel your stall speed will decrease.  In this case, the indicated airspeed at which you stall will change since the weight of the plane is decreasing.

Some people may say that knowing aerodynamics in this sort of detail is cumbersome and unnecessary for flying an airplane–and perhaps it is.  But knowledge is power, and in an emergency all those hours on the ground building your expertise may just make the difference.

Further Reading:
Wikipedia: Stall
Factors affecting stall speed
Eckhard’s great explanation of why stall speed increases with weight

(Unfortunately it rained last Friday and today, and both days I was unable to go for my lesson.  I have only been able to attend 2 of the 5 lessons I’ve scheduled so far because of bad weather!)