V_X

V_X means speed for best angle of climb.

Source: 14 CFR 1, §1.2

• When the airplane is in steady flight with moderate angle of climb, the vertical component of lift is very nearly the same as the actual lift. Such climbing flight would exist with the lift very nearly equal to the weight. The net thrust of the powerplant may be inclined relative to the flight path but this effect will be neglected for the sake of simplicity. Note that the weight of the aircraft is vertical but a component of weight will act along the flight path.
• If it is assumed that the aircraft is in a steady climb with essentially small inclination of the flight path, the summation of forces along the flight path resolves to the following:
$$\mathrm{Forces\; forward}=\mathrm{Forces\; aft}$$ $$T=D+Wsin\gamma$$

where:

T = thrust available, lbs.

D = drag, lbs.

W = weight, lbs.

γ ("gamma") = flight path inclination or angle of climb

Source: Air Training Command Manual 51-3, page 152

• This basic relationship neglects some of the factors which may be of importance of airplanes of very high performance. For example, a more detailed consideration would account for the inclination of thrust from the flight path, lift not equal to weight, subsequent change of induced drag, etc. However, this basic relationship will define the principal factors affecting climb performance. With this relationship established by condition of equilibrium, the following relationship exists to express the trigonometric sine of the climb angle, γ:
$$sin\gamma =\frac{T-D}{W}$$
• This relationship simply states that, for a given weight airplane, the angle of climb (γ) depends on the difference between thrust and drag (T - D), or excess thrust. Of course, when the excess thrust is zero (T - D = 0 or when T = D), the inclination of the flight path is zero and the airplane is in steady, level flight. When the thrust is greater than the drag, the excess thrust will allow a climb angle depending on the value of excess thrust. Also, when the thrust is less than the drag, the deficiency of thrust will allow an angle of descent.

Source: Air Training Command Manual 51-3, page 152

• The maximum angle of climb would occur where there exists the greatest difference between thrust available and thrust required, i.e., maximum (T - D). [The figure] illustrates the climb angle performance with the curves of thrust available and thrust required versus velocity. The thrust required, or drag, curve is assumed to be representative of some typical airplane configuration which could be powered by either a turbojet or propeller type powerplant.
• The thrust available curves for the representative propeller aircraft show the typical propeller thrust which is high at low velocities and decreases with an increase in velocity. For the propeller powered airplane, the maximum excess thrust and angle of climb will occur at some point just above the stall speed. Thus, if it is necessary to clear an obstacle after takeoff, the propeller powered airplane will attain maximum angle of climb at an airspeed conveniently close to — if not at — the takeoff speed.
• The thrust curves for the representative jet aircraft show the typical turbojet thrust which is very nearly constant with speed. If the thrust available is essentially constant with speed, the maximum excess thrust and angle of climb will occur where the thrust required is at a minimum, (L/D)_MAX. Thus, for maximum steady-state angle of climb, the turbojet aircraft would be operated at the speed for (L/D)_MAX.

Source: Air Training Command Manual 51-3, page 152