Aircraft Climb Performance

One of the most important aspects of aircraft performance is the ability to climb. Because cruise performance is enhanced at high altitudes, a quick climb is important to maximize efficiency. Safe obstacle clearance is obviously an important consideration in climb, but noise abatement is also a critical factor. Aircraft must climb steeply for safe obstacle clearance as well as to avoid undue noise to those who live near busy airports.

Let's examine the various components of climb performance. An aircraft can climb only if it can produce excess thrust. This excess is the pounds of thrust force being produced beyond that needed to overcome drag. For example, if an aircraft is producing 1,000 pounds of thrust and has 700 pounds of drag, it would have 300 pounds of excess thrust available. In a climb, a component of weight acts rearward along the flight path. The steeper the climb angle, the greater this component. In a steady-state climb, meaning the climb angle is constant and the airspeed is not changing, the forward-acting thrust must equal the rearward-acting forces of drag plus the weight component. The greater the excess thrust, the steeper the possible climb. Jet fighters capable of producing more thrust than they weigh can climb at a 90-degree angle--straight up. To perform this vertical climb, the amount of thrust created must equal the drag the aircraft is experiencing as well as the entire weight of the aircraft. If a jet aircraft has more thrust available than the sum of weight and drag, not only could it climb straight up, it could also accelerate its airspeed while climbing. To maximize excess thrust, a jet-powered aircraft will climb at a speed where drag is minimum. This is called the best angle of climb speed, abbreviated Vx. In the case of a reciprocating aircraft, the amount of thrust produced decreases with airspeed due to the decreasing angle of attack on the propeller. Because more thrust is produced at lower airspeeds, the Vx speed for a reciprocating aircraft is much closer to stall speed than for a turbojet. To calculate an aircraft's climb angle, take the inverse sine of the excess thrust divided by the aircraft's weight. Climb Angle = Sin^-1(Thrust-Drag/Weight).

The opposite of a climb is a descent. As excess thrust is necessary for a climb, a descent is the result of deficit thrust. The most critical descent is the emergency engine failure power-off glide. Most student pilots can tell you that this glide is done at the minimum drag airspeed, but cannot explain much more. The reason for this speed is that in a power-off, zero-thrust situation, any drag represents deficit thrust. Assume that an aircraft is experiencing 500 pounds of drag at an airspeed of 80 knots--this means that the aircraft has 500 pounds of deficit (negative excess) thrust. By plugging the numbers into the formula above, the descent (negative climb) angle can be calculated. If this aircraft slowed to 60 knots and had a decrease in drag to 400 pounds, the descent angle would also be decreased. When flying at the lowest possible drag speed, the least possible descent angle is attained, and therefore the longest glide.

An interesting thing about best glide speed is that it is always found at the same angle of attack (AOA) regardless of aircraft weight. Because every angle of attack has a corresponding coefficient of lift (Cl), and a corresponding coefficient of drag (Cd), finding the AOA that results in the highest ratio of these two is the [Cl/Cd]_maxAOA. At this and only this angle of attack will the aircraft experience its best glide. The glide angle is a function of this [Cl/Cd] ratio. Because this ratio does not change with weight, neither does the glide angle. What does change is the airspeed at which this angle of attack is flown. The higher the weight, the faster the airspeed, but the descent angle will be the same angle. To see how the speed changes, multiply the square root of the weight ratio by the old airspeed. V2=V1. If, if in an exaggerated example, the aircraft's new weight is four times the old weight, the new speed is twice the old speed, since the square root of four is two.

With all this talk of excess thrust, one might ask, what does lift have to do with climbs? Many pilots wrongly think it is excess lift that makes an aircraft climb. When transitioning into a climb the flight path is curved upward. Imagine starting in level flight and transitioning into a three-degree climb angle. The flight path is a straight line in level flight, and a straight line when established in the climb, but in between it is curved upward. Isaac Newton said that to deflect an object's path, an outside unbalanced force must be applied, in this case excess lift. Assume in level flight that both lift and weight are 10,000 pounds; if the pilot pitches the nose upward and increases the angle of attack, this produces more lift, say 11,000 pounds. There are now 1,000 pounds of excess unbalanced lift in the vertical direction that curves the flight path upward. In the lateral, when banking the aircraft, the horizontal component of lift is what accelerates or turns the flight path. The greater the horizontal lift component, the tighter the radius of curvature. Similarly, the greater the excess lift, the tighter the radius of curvature upward. If deficit lift is encountered, the flight path will curve downward until all the forces are in balance in an unaccelerated descent at a constant angle and speed.

One can summarize by saying excess lift deflects the flight path upward and excess thrust sustains the flight path once deflected. Even a light training aircraft can attain an impressive climb angle by diving to gain airspeed, and then pitching up. If this angle is greater than what the excess thrust can sustain, the airspeed will decrease until the eventual stall.

Another way to measure a climb is by the rate (feet per minute) rather than the angle of ascent. The ability of an aircraft to climb in terms of rate is a function of excess power. You may recall from physics that power is defined as the rate at which work is done. Work, you will recall, is a force applied through a distance. To lift a 600,000-pound jet to an altitude of 10,000 feet takes six billion foot pounds of work (600,000 pounds x 10,000 feet). To complete this climb in 10 minutes (or 600 seconds) would require 10,000,000 foot pounds per second of power (6,000,000,000 foot pounds/600 seconds). Thanks to British physicist James Watt, who determined that a horse is capable of producing roughly 550 foot pounds of power per second, we can express this figure in terms of horsepower. In our example, the amount of power required would be a little more than 18,000 horsepower.

An aircraft's maximum rate of climb occurs at an airspeed where there is maximum excess thrust horsepower. The best rate of climb speed, abbreviated as Vy, is at a faster speed than Vx. For each climb the pilot must determine whether it is more important to climb at the steepest angle to clear obstacles, or at the fastest rate. To calculate an aircraft's climb rate in feet per minute, multiply the constant 33,000 by the excess thrust horsepower divided by weight. ROC=33,000[(THPavailable-THPrequired)/Weight].

Because thrust and power are not the same thing, the airspeed where maximum excess thrust is available (Vx) is not necessarily the same as the airspeed where maximum excess thrust horsepower is available (Vy). As an aircraft climbs, the thrust and power available and required curves shift. Because of this, the speed where maximum excess thrust is found increases and the speed where maximum excess thrust horsepower is found decreases. In other words, as one climbs, Vx and Vy converge, even though the maximum angle and rate of climb both decrease with altitude. At the absolute ceiling of the aircraft these two speeds are equal. The absolute ceiling of an aircraft is a theoretical limit as this is the highest altitude an aircraft could fly. All thrust available is necessary to sustain level flight--any slower and the aircraft will stall. The service ceiling is a more useful figure; this is the altitude where an aircraft can still climb at 200 feet per minute.

FAA regulations require jet transport aircraft to be able to sustain minimum climb gradients immediately after takeoff with an engine failure factored in. The gradient depends on how many engines the aircraft is certified with. For example, a two-engine aircraft such as a Boeing 737 must be able to climb from 35 feet to 400 feet with a climb gradient of 2.4% on just one engine with flaps in the takeoff position. To compare, a four-engine jet such as a Boeing 747 must be able to climb with a 3.0% gradient. Jet transport aircraft expedite their climb to 1,500 feet while retracting flaps and slats. Above this altitude a climb profile such as 250/280/.72 is maintained. This means that the aircraft climbs at 250 knots while speed-restricted below 10,000 feet, then holds 280 knots until that speed yields a mach number of 0.72 (72% of the speed of sound). This altitude is called the mach cross over altitude. The mach number is held constant until reaching the assigned cruise altitude.

From aerodynamics to regulations, there's a lot more to climbs than just increasing altitude. One thing's for sure, if it were not for the ability to climb, a jet transport would just be a fast bus with wings!

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