Math is Fun
Basically all the engine data comes from Lycoming in this case. The data is "empirical" from test (Dyno and flight) they did to certify the engine. However lucky for us they follow a predictable trends and relationships.
LYCOMING POWER DATA:
Lycoming presents the data in two forms a table for a few set of spacific percentage power, usually 55%, 65% and 75%. This is useful and you can just read it right off the table and do some interpolation in between. These are not great because they only standard DAY conditions (temps) and a few spacific power settings. It is a good tool in the cockpit.
The other method Lycoming presents the data (Usually found in the Lycoming operators manual you can purchase) is a thing engineers called a Nomogram. A may recall seeing one. It has a series of curves on one chart that projects over to another chart with curves. Knowing the biggies, RPM, MAP, OAT you can calculate percentage power and fuel flow. It works backwards and knowing enough "Unknowns" you can solve for the knows. It is very accurate and has corrections for "Non standard" day temps. However it is cumbersome to follow the plot and read it, especially in a plane. If you are a solo pilot I would not go head down that long.
This key reprint shows the two types:
Lycoming Power Chat and nomagram
Also related:
Reading Lycoming power tables
STANDARD ATMOSPHERE, DENSITY ALTITUDE AND TRUE AIRSPEED
As far as atmosphere, there is basic "altimetry ". Which most pilots are exposed to in basic training: Pressure Altitude and Density altitude for example. Most Private pilots don't get into the formulas and physics of the atmosphere. All they do is go into their E6B or aviation calculator and enter the needed "knowns" to get the solution. We all should have been exposed to calculating density altitude. There are formulas to calculate standard atmosphere and corrections. Properties like barometric pressure, pressure altitude, temp and humidity are usually needed. We usually omit humidity in our calculations, but it does affect air density. (Wet air is less dense right). Humidity has a smaller effect than temp and pressure.
The other think we should know how to get TAS, true airspeed. Again most just input indicated airspeed, Baro and temp and the answer pops out the E6B. There are formulas for this also, but most pilots just use a E6B "computer" (circular slide rule or electronic) which is programed with the equation.
Where are the formulas for true airspeed or density altitude? They are in basic aerodynamic text books or on the web. There is a thing called "Standard Atmosphere" which engineers and scientist use as a bench mark. Its a basic model of the atmosphere. Every thing comes off that "STANDARD". There are formulas for standard atmosphere, TAS and density altitude.
Any data can be fit to equations, some data better than others.
SPREAD SHEETS
Now Kevin Horton's engine power spread sheet is cool. He is a clever devil. I have it, and I recall he used the tabular data from Lycoming and does a "Data Look-up". The Excel program takes a table of data (matrix) and "interpolates" the table or tables for the answer. I have a HP IPaq, a hand-held computer that uses MS Pocket PC software and has a Excel spread sheet program. Frankly I have the standard power settings memorized for the few power settings I use most of the time. I only care I am below 75% power. Most of the time I just set a standard setting RPM/MAP like 25/25 for climb. With spread sheets it is easy to just dump the Lycoming data in and have it look it up. If you have a simple programmable calculator a formula is better.
There are no official formulas for calculating percent engine power but it would be easy to come up with some. You just take the curves that Lycoming provides and "CURVE FIT" them to an equation. You can fit them to differnt type equations, such as a logarithmic or polynomials. It gets a little complicated because you have RPM/MAP/ALTITUDE/TEMP. The output would be HP and Fuel Flow.
There is engineering software that will do this curve fitting, like Mathematica, or you can do it manually with some basic calculus and iteration. You would probably get a good "FIT" and correlation but it would be approximate. May be 1% off. Close enough. I don't care enough to do that. I much prefer to make a little laminated card with the tabular 55%, 65% and 75% power and have that tucked away on the side of needed.
I have my own spread sheets that calculate engine power, standard atmosphere, corrections to standard day conditions, total drag and propeller efficiency. You can write your own. It is easy.
Pierre's DATA
As far as Pierre's data he left out the Barometric pressure setting and Manifold pressure, so I made some assumptions. I assumed the pressure was 29.92. I know his density altitude was about 9,800 ft with the data he provided, 8,500 ft indicated and 50F OAT. I also assumed that his manifold pressure was about equal to the local atmospheric pressure to -0.50" hg under those flight conditions, or about 20.6 to 21.1 inches hg. That is why it is important to include all the parameters, other wise its a guess. However his data correlates well with the known performance, so his numbers and my guesstimates are in the ball park.
Hope this answers your questions. If you want to learn more about standard atmosphere, aerodynamics or curve fitting just google it.
George
