Stalling Speed

Подпись: VStall _ Подпись: pSC Stalling Speed

The curves shown in Fig. 9.4 are extended into a low speed-range that is not actu­ally accessible to the clean Bf-109G. The airplane probably would not fly in its clean configuration at a speed of less than about 90 mph. This stalling speed can be esti­mated by using the largest possible lift coefficient that reasonably could be expected without deflected flaps or slats. When we solve Eq. 9.5 for the flight speed for a given maximum lift coefficient, the result is:

If a value of CL max = 1.4 is used in this result, the minimum (i. e., stalling) flight speed at sea level in the clean aerodynamic condition is about 104 mph. The need for flaps and other high-lift devices is clear because this is an uncomfortably high speed at which to land an airplane.

Speed for Minimum Thrust Required

Подпись: dTR dq Подпись: Do Stalling Speed Stalling Speed Подпись: (9.11)

Notice that there is a special speed at which the thrust required is a minimum. It is clear (see Eq. 9.6) that this condition corresponds to the speed at which the L/D ratio is maximum. It is curious that this occurs at the point where the induced and parasite drags are exactly equal. The reason for this becomes clear if we determine the condition for a minimum value by taking the derivative of the thrust required with respect to the speed (or corresponding dynamic pressure) and setting it equal to zero. We find:

which shows that for minimum thrust required we must have:

CDo = CDi,

Подпись: ^minT™ Подпись: W / S

as shown graphically in Fig. 9.4. What is important from a performance standpoint is that the speed we must fly to reduce the thrust (and drag) to a minimum corresponds to the condition of Eq. 9.11. Solving for the value of dynamic pressure, q, that cor­responds to the minimum, we find:

Do

Подпись: VminTR = V (L / D)n Stalling Speed Подпись: (9.12)

and the associated flight velocity is:

This flight-speed information is important in the effective operation of an air­plane because flying at maximum L/D ratio (i. e., minimum drag or thrust required) is required to achieve the maximum range or minimum fuel consumption, as demonstrated in a subsequent subsection. For the Bf-109G at sea level, Eq. 9.12 yields a value of about 210 ft/sec (143 mph), as indicated in Fig. 9.4. Notice that this speed changes with altitude, as indicated by the appearance of density in Eq. 9.12.

We now can determine the maximum L/D ratio for the Messerschmitt Bf-109G. This is easy because it is clear that the drag coefficient is equal to twice the parasite – drag coefficient at the best L/D speed. We take the ratio of the lift and drag coefficients and insert the value for the best speed from Eq. 9.12; the result is:

Подпись: (9.13)(L) = 1 jne AR

‘D ‘ max 2 у Cd0

which yields a value of about 12 for the Bf-109G:

= 12.1 for Bf – 109G.

max

If a pilot suffers an engine failure, he or she should glide at 143 mph to achieve the best chance to find a suitable field for a successful off-field landing. Flying slower may increase the time in the air but results in less distance covered in search of a good landing field.

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