Читать книгу Flight Theory and Aerodynamics - Joseph R. Badick - Страница 31

Newton’s laws of motion express relationships among force, mass, and acceleration, but they stop short of discussing velocity, time, and distance. These are covered here. In the interest of simplicity, we assume here that acceleration is constant. Then,

where

 Δ (cap delta) means “change in”

 Vf = final velocity at time tf

 Vi = initial velocity at time ti

If we start the time at t_i = 0 and rearrange the above, then

(1.4)

If we start the time at t_i = 0 and V_i = 0 (brakes locked before takeoff roll) and rearrange the above where V_f can be any velocity given, for example liftoff velocity, then

The distance s traveled in a certain time is

where the average velocity V_av is

And incorporating Eq. 1.4, and substituting for V_f, we get

which yields

(1.5)

Solving Eqs. 1.4 and 1.5 simultaneously and eliminating t, we can derive a third equation:

(1.6)

Equations 1.3–1.6 are useful in calculating takeoff and landing factors, and are studied in more detail in Chapters 8 and 9.