The standard RoC formula (using FPM and LBS) usually shows the excess HP at sea level at max gross to be around 33% of the rated HP for most GA propeller aircraft.
The formula is ROC in FPM = ExcessHP*33,000*Propeller efficiency divided by All up Mass in LBS. The formula is derived from the power available and power required curves.
However, something must happen to the curves as you climb, assuming that the only change is density altitude, not mass. The TAS of Vy will increase (and Vy converges on Vx with altitude, becoming the same at absolute ceiling), and Power required is linked to TAS, but as density decreases parasite drag will reduce for a given IAS. At the same time as you reduce Vy with density altitude it presumably doesn’t move up the backside of the power required curve, but conversely Vx is presumably moving down the curve – induced drag increases at a much faster inverse rate than parasite drag.
If this improvement did not occur then most normally aspirated propeller aircraft would have a service ceiling of around 9 – 10,000 feet, which is roughly where full throttle 65% power lies (ie 1 minus the 33% excess power at sea level). However most of the NA class manage around 13 – 15,000 feet as a service ceiling, and some draggy aircraft, the 150 HP Super Cub, have a 20,000 foot service ceiling. Don’t laugh, a 135 HP Super Cub held the altitude record for many years for one of the SEP classes (around 31,000 feet).
The calculus for figuring out a service ceiling must be quite interesting, if you are that way inclined, and hopefully someone comes along to help understand this.
I fear I have posted this question before – although it drifted quite nicely into pressurised magnetos!
Apologies for the senior moment, but I don’t think we got an answer the last time in the HP loss DA thread which the forums wonderful algosomething picked up on as a related thread.
How do you figure out excess HP with fixed pitch propeller? Such a number makes no sense other than perhaps with a perfectly pitched climb propeller.
LeSving wrote:
How do you figure out excess HP with fixed pitch propeller? Such a number makes no sense other than perhaps with a perfectly pitched climb propeller.
Of course it makes sense! How to figure it out is another thing.
RobertL18C wrote:
but as density decreases parasite drag will reduce for a given IAS.
At a first approximation Vy will remain the same (as an IAS), induced and parasitic drag (the forces) remain the same, as those are actually dependent on TAS and density (which conveniently reduces to IAS). HOWEVER, the power needed to overcome those forces goes up by the TAS. The power to overcome drag is TAS^3 * RHO and this means that as you climb (assuming you can maintain sea level power) the excess power declines. Unfortunately there is also a substantial change in advance ratio for the propeller and blade angles will materially change the propeller efficiency (they tend to be low at Sea Level Vy)
Airborne_Again wrote:
Of course it makes sense
I don’t see how. Excess compared with what? With a fixed pitch, max HP is dependent on airspeed because the max obtainable rpm varies with airspeed. I would say the climb formula only makes sense with a cs prop.
Robert,
After a looking at my aircraft performance data, it shows a couple of things
1 – Excess power at Vy and sea level is about 35% of rated power, but actually 45% of the effective power. That is after allowing for Prop Efficiency.
2 – Prop efficiency improves by 9% in the climb, therefore ‘creating extra power’
3 – I have assumed engine power drops directly with air density – normally aspirated, CS prop and no allowance for any marginal ram effect as the TAS increases. (The actual aircraft is TN and has a 25000 ft regulatory ceiling)
On this basis, I get my actual climb performance and a ceiling of about 14000 feet. However, Vy decreases with altitude and converges to just above the sea level Vx. Factoring in the reducing Vy, gives a calculated service ceiling of about 18000 feet, about the same as the book value. So the formula works, but you need to include the changing prop efficiency, the changing Vy and recognition that the excess power is of rated power not effective SL Vy power.
It will work as well with fixed pitch, but with the added complication that the power output of the engine will change with rpm, which will change due to changes in prop efficiency, true airspeed and air density (as it relates to propeller ‘indicated rotational airspeed’ as well as engine volumetrics).
LeSving wrote:
I don’t see how. Excess compared with what? With a fixed pitch, max HP is dependent on airspeed because the max obtainable rpm varies with airspeed. I would say the climb formula only makes sense with a cs prop.
Compared to what is necessary for level flight, of course! I think you are confusing “difficult to know/compute” with “meaningless”.
Airborne_Again wrote:
Compared to what is necessary for level flight, of course! I think you are confusing “difficult to know/compute” with “meaningless”.
I just don’t see how it can be used in any meaningful way in that formula, because the excess power is not a “constant” like it is for a CS prop. Therefore it is no meaningful way to define excess power.
For a constant speed prop, the thrust is simply power*efficiency/airspeed. You “move” on the top of the curves, and the reason you can do that is because the HP is constant (independent of airspeed). For a fixed pitch, you only move along one single curve, and in addition, the HP increases with airspeed (up to a point). The “excess power” will be at a different speed than the speed you want to calculate it at.
Excess power for a fixed pitch prop is something very different (physically) than excess power for a CS prop.
mm_flynn why does this effect the service ceiling? Power required increases with TAS and therefore you need to drift down the power required curve to seek a new max excess power point, but with altitude the power available curve is reducing until eventually you reach zero excess power, and you are flying at minimum power speed which approximates Vx – and is quite close to stall speed.However, Vy decreases with altitude and converges to just above the sea level Vx.
To LeSving’s point and going to the source of his propeller efficiency graph (Aerodynamics for Naval Aviators), this excellent book available for free on the FAA website, states
In an ideal sense, if the propeller efficiency were constant, maximum rate of climb would occur at the speed for minimum power required. However, in the actual case, the propeller efficiency of the ordinary airplane will produce lower power available at low velocity and cause the maximum rate of climb to occur at a greater speed than that for minimum power required.
I think the point being that even with constant speed, propeller efficiency is not constant.
Looking at the question from a different perspective, aircraft with quite a large difference between Sea Level Vx and Vy (for example the fixed pitch Super Cub 150 HP – 45 mph and 75 mph respectively) seem to have unusually high service ceilings for their power loading (12lbs/hp) while aircraft with less of a spread between Vx and Vy at Sea Level, the 172S (14 lbs/hp) for example is 62 knots and 74 knots, respectively, have much lower service ceilings – 13,500’ vs 20,000’.
