Principal Air - Flight Training / Charter in Canada

Principal Air - Flight Training / Charter in Canada, Learn to Fly


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The Climb

“It’s wonderful to climb the liquid mountains of the sky.

Behind me and before me is God and I have no fears.”

-Helen Keller 

The essence of an aircraft is that, given the correct inputs, it can lift itself off the ground and take to the air. It is a machine that, miraculously, allows us mere humans to move above the surface of our planet in that great sea of air giving us a view of the world enjoyed by only a few, fortunate souls. Without the capability to climb, an aircraft would merely be an expensive bus with parts sticking out making passage through traffic a sore trial.

The ability of an aircraft to climb is termed its climb performance, and there is a great range in climb performance from one aircraft type to another. Some aircraft we think of as having great climb performance. An F-16 fighter aircraft, for example, according to the Lockheed Martin Corporation, climbs at 50,000 feet per minute at sea level. Some aircraft demonstrate less exciting climb performance. I’ve watched my little 100 hp Champion Citabira climb out at a blistering rate of 2-300 feet per minute when loaded to gross weight on a warm day.

We rely on our aircraft’s climb performance for a number of purposes. Initially, we must move the machine from the ground to the air. We must then be able to clear obstacles in our path, and we must be able to achieve sufficient altitude for a given flight. Perhaps, we might be flying from the coast to an inland destination and, checking our charts, we see there are mountains in our way.

Additionally, as altitude increases true airspeed also increases allowing us to fly faster over the ground and maximize the efficiency of our engine, increasing our range. Reaching an appropriate cruising altitude as soon as possible has considerable advantages.

A number of generic factors affect the ability of any aircraft to climb including the weight of the aircraft, the location of its centre of gravity, density altitude and humidity, use of carburetor heat, deployment of flaps and landing gear, turbulence and the pilot’s accuracy and skill in maintaining correct angle of attack and airspeed.

An aircraft climbs proportionally to excess thrust or total available thrust minus total drag, and inversely in proportion to weight. With propeller driven aircraft, best rate of climb is achieved at the speed that produces maximum excess thrust horsepower (ETHP). ETHP is thrust horsepower produced by the engine/propeller beyond that required to maintain level flight. The aircraft’s rate of climb (R/C), how quickly it gains altitude, expressed in feet per minute (fpm), can be derived from the formula: R/C = ETHP x 33,000/Weight (1).

We see from the formula that increasing the weight of an aircraft is a significant factor. Doubling the weight will cut our rate of climb in half. A lighter aircraft will out-climb its heavier sister in direct proportion to the difference in weight.

The location of the centre of gravity also affects rate of climb. An aircraft with a more forward centre of gravity finds itself at a disadvantage to an identical aircraft at the same weight with a more aft centre of gravity. Moving the centre of gravity forward requires additional down-force developed by the tail-plane. This down-force acts on the aircraft like weight and, effectively, increases the total weight of the aircraft.

Density altitude significantly affects the climb performance of an aircraft. High density altitude, the performance altitude at which the machine is operating, reduces climb performance. Humidity, which can be factored into density altitude, also reduces performance primarily through adversely affecting engine performance. High humidity results in reduced power output and thus reduced ETHP. A humid day with high density altitude may seriously decrease our ability to climb

Use of carburetor heat reduces power output from the engine which, in turn, reduces climb performance. Flaps increase lift but also increase drag. Use of flap on takeoff may shorten our ground run, but we pay for that advantage as soon as the wheels leave the surface. Increasing drag effectively reduces ETHP.

Landing gear, if you fly a machine capable of retracting its gear, also increases drag and thus reduces available excess thrust. To maximize climb performance with a retractable gear aircraft, let’s get that gear up as soon as safely possible 

Angle of attack is critical to achieving climb performance. With a propeller driven aircraft, the amount of available thrust decreases with airspeed due to the decreasing angle of attack on the propeller (2). Increased airspeed rapidly increases parasite drag produced by the airframe.  

To achieve maximum climb performance in terms of time, it is necessary to maintain an angle of attack resulting in best rate of climb speed, Vy. In terms of maximum altitude in relation to distance, we must maintain an angle of attack producing our best angle of climb speed, Vx. Turbulence and pilot skill both affect how well an aircraft maintains the correct angle of attack and thus airspeed to achieve best rate or best angle of climb.

Increasing or decreasing airspeed (angle of attack) above or below Vy or Vx decreases climb performance. 

To minimise unpleasant surprises, if we do find ourselves flying in turbulent conditions, it would be an excellent plan to consider reduced performance in any calculation regarding obstacle clearance or time and distance to a given altitude.

 It is important to note that Vy and Vx are not constant, in terms of IAS, as an aircraft gains altitude. A look at your machine’s POH will give you some clues about this process. The 1976 C-172 POH, for example, recommends a best rate climb speed of 78 KIAS at sea level reducing to 75 KIAS at 3000’, 72 KIAS at 6000’ and only 68 KIAS at 10,000.

The speed and angle of attack for Vy is dependent on maximum excess thrust horsepower (excess power) and thus decreases with altitude. Vx, our best angle of climb speed, is dependent on maximum excess thrust (excess force). IAS for best angle of climb increases as we gain altitude.

Vy and Vx eventually converge as we approach our absolute ceiling, the altitude at which the machine’s ability to climb at full power reaches zero.

A Rule of Thumb for estimating the decrease in Vy with altitude is to reduce indicated airspeed by 1% or 2 knots for each 1000’ increase in altitude above sea level, excluding the first 1000’ (3). For Vx, a good Rule of Thumb is to increase indicated airspeed by ½% or 1/2 knot per 1000’ or, more simply, 1 knot per 2000’ increase in altitude (4).

To establish a cruise climb, the angle of climb we might use once we have achieved a safe altitude and are heading out on a cross country flight, we can simply add the difference between best angle of climb speed and best rate of climb speed to best rate of climb speed (5). For the C-172, for example, at 3000’ the best rate of climb is 76 KIAS best angle of climb is 60 KIAS; 76 – 60 + 76 = 92. We can use this speed to maximize our distance made good and, at the same time, maintain a reasonable rate of climb.

Contrary to what many people suppose, climb is not produced by excess lift. Initially, pulling the nose up to enter a climb does briefly produce excess lift resulting in vertical acceleration. Once established in a steady state climb, however, it is excess thrust that causes an aircraft to climb, as our formula shows. In a steady state climb our angle of attack will be identical to that for the same aircraft in level or descending flight at the same airspeed, assuming identical weight, centre of gravity location and environmental conditions.

Intuitively, we might think that because we see a nose up attitude in a climb that our angle of attack must be greater than when flying straight and level. We don’t want to confuse angle of climb with angle of attack or rate of climb, however.

Angle of climb is the angle of our flight path measured in relation to the horizon. Angle of attack is the angle described between the chord line of the wing and the relative wind. Our vertical speed, our rate of climb, is the aircraft’s vertical velocity measured at right angles to the horizon (6).

We can say that, in a climb, our attitude is a measure of our angle of climb plus our angle of attack. If, for example, in straight and level flight we maintain an angle of attack of, say, 7 degrees at a given airspeed, on entering a climb at an angle of 5 degrees at the same airspeed—about typical for a light, training aircraft—our climb angle is now 5 degrees but our attitude in relation to the horizon is 7 + 5: 12 degrees

So, do I as a pilot really need to know this stuff? Perhaps not. Understanding the machine’s POH and allowing, always, a margin for safety normally does the job just fine. Many people seem to fly happily and safely year in and year out without knowing very much at all. It is pretty cool stuff, however. I always figure you can know too little, but it’s impossible to know too much. The more we dig and learn about this miracle we call flight the more interesting and compelling it all becomes. Enjoy.

Notes:1.       Kershner, William K., The Advanced Pilot’s Flight Manual, Iowa State University Press, 1994, page 90. We can work this formula backward and determine that a C-172 which climbs at 645 fpm at gross weight at sea level can develop approximately 45 excess thrust horsepower at best rate of climb speed. One horsepower equals 550 ft lb/sec or 33,000 foot pounds/min.

  1. Esser, Dave, “Aircraft Climb Performance,” Woman Pilot Magazine, August 2002.
  2. Flight Training Manual, 4th Edition Revised, pg 55.
  3. Kershner, William K., The Advanced Pilot’s Flight Manual, Iowa State University Press, 1994, page 94.
  4. ibid, pg 93
  5. For those who enjoy them, the formula for angle of climb (c) is c =sin-1( Tx/W), where Tx represents excess thrust or total thrust minus total drag, and W represents weight. Thrust (Tx) can be derived from the formula THP = TV/325 where T represents the amount of thrust produced by the propeller, V represents KTAS and 325 is a constant used for knots. In the case of our C-172 climbing at 78 KTAS, we can see that the propeller at best rate of climb is producing approximately 187 lbs of thrust and that sin c = .0813. Or, more simply, we might say, c = sin-1 Rate of Climb/TAS. For a C-172 at gross weight at sea level with a TAS of 78 knots (approx. 7904 fpm) and a rate of climb of 645 fpm (POH), this gives us a best rate climb angle of approximately 5 (645/7904 = .082; sin 5  = .087).