Best Angle and Best Rate of Climb: VX and VY

VX and VY are the two climb speeds a pilot meets first. VX, the best angle of climb speed, gives the most height for the ground covered and is the speed for clearing an obstacle. VY, the best rate of climb speed, gives the most height in the least time and is the speed for reaching a cruising level quickly.

The two speeds are not interchangeable. Angle and rate depend on different quantities, so they peak at different speeds; they move differently with altitude, mass and configuration; and they meet at the airplane's absolute ceiling. This article explains why, building on the wider subject of climb performance, and shows how light singles, light twins and jet transports use them.

Angle and rate of climb

The climb gradient is the height gained divided by the horizontal distance covered. It is given as a percentage or in feet per nautical mile; because a nautical mile is about 6,076 ft, 1 percent is about 60 ft per nautical mile. The rate of climb is the height gained per unit of time, in feet per minute. The two are linked by speed:

rate of climb (ft/min) = gradient (ft/NM) × groundspeed (kt) ÷ 60

In a steady, straight climb at flight path angle γ, the thrust must overcome the drag and also carry a component of the weight up the slope: T = D + W sin γ. Rearranged:

sin γ = (T − D) ÷ W

The angle of climb therefore depends on excess thrust, thrust available minus drag, divided by the weight. Lift now balances only W cos γ, so in a steady climb it is slightly less than the weight; the thrust carries the rest. The rate of climb is the true airspeed multiplied by sin γ:

rate of climb = (T − D) × TAS ÷ W = (power available − power required) ÷ W

The rate of climb therefore depends on excess power, power available minus power required, where power is force multiplied by speed.

A worked example, with figures chosen only to show the arithmetic, makes the difference concrete. Suppose a light airplane in still air climbs at 650 ft/min at 60 kt and at 750 ft/min at 75 kt. At 60 kt it gains 650 ft per nautical mile; at 75 kt, 750 × 60 ÷ 75 = 600 ft per nautical mile. The slower speed gives the steeper path, the faster one the quicker climb. The first speed behaves like VX, the second like VY.

VX: best angle of climb

VX is the speed at which excess thrust is greatest. Since sin γ is excess thrust divided by weight, at a given weight it gives the steepest path through the air and so the greatest height for the distance flown. It is the speed for obstacle clearance: after a short-field takeoff with trees beyond the boundary, the pilot climbs at VX until they are cleared.

Where VX lies depends on how thrust varies with speed. A jet engine gives roughly the same thrust over the speed range of a climb, so excess thrust is greatest where drag is least: for a jet, VX lies close to the minimum drag speed, VMD. A propeller's thrust falls as speed rises, because the engine delivers roughly constant power and thrust is power divided by speed. The thrust surplus is then greatest at a speed below VMD, so for a propeller airplane VX lies below VMD.

VX is slow. It has the highest nose attitude of the normal climb speeds and the smallest margin above the stall, and in a piston single the low airspeed gives the engine the least cooling air. It is held only while it is needed.

VY: best rate of climb

VY is the speed at which excess power is greatest, and it gives the greatest height in a given time. It is always higher than VX, and the reason follows from the definitions. Excess power is excess thrust multiplied by speed. At VX the excess thrust curve is at its peak, so it is flat: a small increase in speed costs almost no excess thrust but adds speed, and the product keeps rising. Excess power therefore peaks at a higher speed than excess thrust.

For a propeller airplane, if power available were the same at every speed, excess power would peak where the power required is least, at the minimum power speed, VMP, about 0.76 VMD. In practice a propeller's efficiency, and so the power available, rises with speed through the climb range, which moves the peak upward. EASA exam material takes VY as about VMD for a propeller airplane. For a jet, whose power available rises almost in proportion to speed, VY lies above VMD and above VX.

Propeller versus jet airplanes

View full schematic

Jet transport manuals seldom work with VX and VY by name, because the flight management system flies an economy climb schedule (see climb performance). The equivalents are still there. On the Airbus A320, green dot speed, the clean best lift-to-drag speed, gives the maximum climb gradient; the speed for the maximum rate of climb lies between the ECON climb speed and green dot, and because the display does not show it, Airbus suggests the turbulence speed as a rule of thumb. One operator's procedures for the Embraer E190-E2 give VX as roughly VFS, the green dot speed, and VY as roughly VFS + 50 kt (see E-Jet normal procedures).

Effect of altitude: the absolute ceiling

Thrust and power fall with air density. Jet thrust falls roughly in proportion to density; a normally aspirated piston engine loses about 3 percent of its power for every 1,000 ft of density altitude; a turbocharged engine holds its rated power up to its critical altitude. Drag at a given indicated airspeed does not change with altitude, but the power required at that indicated airspeed rises, because the true airspeed is higher. Both surpluses shrink as the airplane climbs, so the gradient and the rate of climb both fall.

The speeds move as well. For a light piston airplane, the indicated VX increases slightly with altitude while the indicated VY decreases by about 1 kt per 1,000 ft, so the two converge. As true airspeeds both rise, VY modestly. For a jet, VX is tied to VMD, which corresponds to a fixed lift coefficient at a given mass; in thinner air that lift coefficient needs a higher true airspeed, so VX rises with altitude as a TAS.

The absolute ceiling is the altitude at which the maximum rate of climb has fallen to zero. Excess power and excess thrust are both zero at a single speed, level flight is possible only at that speed, and VX and VY have become the same speed. The absolute ceiling has little practical use, because the rate of climb tends to zero as it approaches and the airplane would take an infinite time to reach it.

The service ceiling is the practical figure: the altitude at which the best rate of climb has fallen to a small, specified value, so that a usable climb remains.

EASA texts give these ceilings as pressure altitudes. The FAA's Pilot's Handbook of Aeronautical Knowledge defines the service ceiling as a density altitude, and FAA multi-engine material does the same for the single-engine service ceiling; the two coincide in ISA conditions. The service ceiling also appears in FAA rules: under 14 CFR 61.31(g), a pilot needs high-altitude training and an endorsement to act as pilot in command of a pressurized aircraft whose service ceiling or maximum operating altitude, whichever is lower, is above 25,000 ft MSL. For a jet transport the usable altitude is limited further by its certified maximum operating altitude and by its buffet margins, which close in at very high altitude.

Effect of mass, flaps and wind

Mass. A heavier airplane needs more lift, and more lift at a given speed means more induced drag. More of the thrust and power goes into simply holding the airplane up, and the smaller surplus is divided by a larger weight, so both the angle and the rate of climb fall, and the service and absolute ceilings are lower. Because the speed at which the wing produces a given lift coefficient varies with the square root of the mass, VX and VY rise as indicated airspeeds, like the stall speed: 21 percent more mass raises them by about 10 percent.

Temperature. Warm air reduces thrust and power, so it reduces both angle and rate; a colder than standard day improves them.

Flaps, gear and bank. Extending flaps increases lift but increases drag proportionally more, so the maximum lift-to-drag ratio falls and the best climb angle is reduced. Flap also moves VMD, and the speeds tied to it, lower (see power curves and speed stability). Takeoff flap therefore shortens the ground run at the cost of a shallower climb, and with an obstacle close ahead the flight manual's distance to 50 ft for each setting decides. Landing gear adds drag with no benefit, and a turn raises the lift needed: the load factor is 1.04 at 15° of bank and 1.15 at 30°, and the extra induced drag reduces the rate of climb.

Wind. A steady wind does not change the airspeed-based performance: the rate of climb, the gradient through the air and VY are the same. It changes the gradient over the ground:

ground gradient ≈ air gradient × TAS ÷ groundspeed

An airplane with an air gradient of 10 percent at 70 kt TAS into a 10 kt headwind has a groundspeed of 60 kt and a ground gradient of about 11.7 percent. With the same wind behind it, the groundspeed is 80 kt and the ground gradient about 8.8 percent. A downwind departure toward rising ground is therefore penalized twice: a longer takeoff run and a flatter climb.

Using VX and VY in practice

Light singles. The flight manual gives VX and VY; neither is marked on the airspeed indicator. A takeoff distance chart that assumes the short-field technique, with the stated flap, full power before brake release, rotation at the stated speed and a climb at VX, does not apply to a normal takeoff and a climb at VY, which need more distance. Once the obstacle is cleared the pilot accelerates to VY. Many flight manuals give a normal or cruise climb speed a few knots above VY, accepting a small loss of rate for better engine cooling, a lower nose attitude with a better view ahead and more margin above the stall in turbulence.

Light twins. Twins add one-engine-inoperative versions: VXSE, the best angle, and VYSE, the best rate of climb or least rate of descent, marked by the blue radial line on the airspeed indicator for maximum weight at sea level. Losing one engine halves the power available but leaves almost all the power required, and the failed engine, the deflected rudder and any sideslip add drag, so the excess, and with it the climb, falls by about 80 percent or more. After an engine failure the pilot flies VYSE, or VXSE while an obstacle must still be cleared (see light twin engine-out performance).

Jet transports. After takeoff a jet climbs at a speed tied to V2 up to the acceleration altitude, then accelerates and retracts its flaps (see takeoff climb segments). In the en route climb the best-gradient speed is the one to use when a steep climb is needed, for example to meet a demanding SID gradient; Airbus advises A320 crews not to reduce to green dot at high altitude, particularly at heavy weight, because accelerating back to the ECON Mach number can take a long time.

ATC. When ATC requires a rapid climb through a level, the A320's expedite function targets green dot, the best-gradient speed, and is meant only for short-term tactical use; for the best overall economy the crew returns to the ECON climb speed.

Library articles are written for study and exam preparation. They do not replace your aircraft's approved documentation, your operator's procedures or the regulations themselves.