ORIGINAL: CrateCruncher

A pilot of a very light (1/2 pound) electric plane is flying in calm conditions at 40 mph

ground speed. A front rolls in changing the conditions to a headwind of 20 mph and a 60 mph

airspeed required to maintain the same ground speed. (1) What is the effect on AOA due to change

in speed AND an added ballast of 3/4 pound? (2) How is control sensitivity effected by the

change in weight at the higher airspeed?


weight(mg)= 0.5 lbm (slugsft/s^2) weird units huh?
wing area= 1.29 ft^2
V1 = 40 mph(58.7 ft/s)
V2 = 60 mph(88.0 ft/s)
airfoil: naca 0006 (cl/AOA data from Abbott, pg.452)
air density (R) = .002378 slug/ft^3

1) Starting with the equilibrium between weight and lift we have:

weight = 0.5*(air density)*(velocity squared)*(wing area)*(lift coefficient)

or

mg = .5R(V^2)S(Cl)

Rearranging terms to get Cl:

Cl = (2mg)/[R(V^2)S]

Airspeed w/o ballast(.5) w/ballast(1.25)
Cl AOA(deg) Cl AOA(deg)
40mph 0.10 1.0 0.24 2.5
60mph 0.04 0.2 0.11 1.0

Notice the AOA of the plane without ballast is very close to zero at the higher airspeed while

the ballasted plane restores the AOA for level flight back to one degree.

2) Sensitivity of +/- 0.5 degree change in AOA at 60mph:

Weight AOA Cl Net Force(Fr) Fr/W*100(%)
0.5lbm +.7/-.3 +.1/-.05 +.7/-1.1 +140/-220
1.25lbm +1.5/+.05 +.2/+.05 +2.4/+.6 +92/-52

Pitching the plane half a degree has a dramatic effect on the plane without ballast. In the last

column the unbalanced reaction force is divided by the total weight of the plane. The

unballasted plane is virtually uncontrollable.