Download Effect of Weight on Stall Speed

Effect of Weight on Stall Speed
© Derek Ruddock Southern Cross Gliding Club, Sydney November 2009
The material below is the opinion of the author and no official endorsement by Southern Cross Gliding, Club or its
Training Panel and instructors, the Gliding Federation of Australia or anyone else is claimed or implied.
What is the effect, if any of weight on the stall speed of a glider?
Ignoring for the moment that a glider is always descending, (even when climbing, it is descending
thru the rising air) we can regard a glider that is not banked for this exercise as flying ‘straight and
level”, ie the glider is not turning. In straight and level flight the weight acting downwards is
(almost) balanced by the lift generated by the wings, and the load factor is 1. The slight discrepancy
is the energy that is being used by the glider to fly.
The lift generated by the wings (and hence the weight) is described by the equation
L=½ρV2SCL
Where L
ρ
V
S
CL
= Lift (or weight)
= Air Density
= Velocity (airspeed)
= Wing area
= Coefficient of Lift
The wing area and the air density are constants for a given altitude and temperature. For unflapped
aircraft, where the shape of the wing cannot be changed, the coefficient of lift can only be changed
by changing the angle of attack of the wing.
In steady flight, lift (L) = weight (W), and W/S is the wing loading N, so rearranging the terms
gives us
N = ½ρV2CL or V = √2N/ ρCL
As the angle of attack increases, the coefficient of lift increases, until the critical angle of attack is
reached, when the wing stalls. This critical angle is a function of the aerofoil of the wing, and is
independent of the wing loading.
What happens to the stall speed if the weight, and hence the load factor is increased?
Using the above equation, if we create a ratio of the old stall speed (Vso ) vs the new stall speed (Vsn
), most of the factors cancel each other out, resulting in the formula
Vsn/Vso = √Nn/No or Vsn = Vso *√Nn/No
In other words, to calculate the new stall speed, take the square root of the old wing loading divided
by the new wing loading, and multiply this by old stall speed
For example suppose we could double the weight of a glider that stalls at 34 knots. What would the
new stall speed be? In this case the wing loading is twice what it was before, and the square root of
2 is 1.414, so the new stall speed is 34 * 1.414, or 48 knots. The weight of a glider cannot double
instantaneously, but if flown into a strong gust, especially if the gust has an upward component, the
load factor can easily double and therefore the stall speed will increase too.
Consider the DG1000 flown solo, at a wing loading of 28kg/m2 where the stall speed is 63 kph (34
knots). If flown dual, where the wing loading increases to 35kg/m2 , the stall speed increases to
√35/28*34, or 38 knots.
What happens to the stall speed of the DG1000 when it is at max take off weight of 750kg? As the
wing area is 17.6m2 , the wing loading is 750/17.6, or 42.8kg/m2 , so the new stall speed is
√42.8/28*34, or 42 knots.