What is the correct term for the type of performance chart where curved lines are followed?

Question

What is the correct term for the type of performance chart where, from a starting location, curved lines are followed to various reference points to eventually find a solution?

For a specific example, the type of chart I'm asking about can be found in the Pilot's Handbook of Aeronautical Knowledge as Figure 11-23:

Background to the question: I would like to reverse-engineer a performance chart in order to use it in a spreadsheet. I have no idea how to do this but if I can discover the name of the type of chart it is, I can begin by looking for notes from other people who have attempted the same.

Answer 1

The correct term is nomograph or nomogram. Thanks Gerry!

Also, thank you to Peter Kämpf and Dean F. for helping to answer my actual question, instead of the one I asked.

Answer 2

After reviewing your profile, I assume you already know what these charts are, how to use them, and for what they are used. If you are trying to derive a spreadsheet for the data, you may want to take a look at TakeOff and Landing Distance tables for similar models. Alternatively, you could derive a program to handle each set of data in each section of the chart separately.

In other words, design a program to:

1. Calculate the pressure altitude based on known field elevations and barometric pressures/altimeter readings in the Kollsman window.
2. Calculate the density altitude based on known pressure altitudes and temperatures.
3. Calculate the ground roll distance of an aircraft based on known density altitudes and aircraft takeoff weights at given lift-off speeds.
4. Calculate the ground roll distance adjustment based on known headwind/tailwind components.
5. Calculate total distance required to clear an obstacle based on known adjusted ground roll distances and obstacle heights.
6. Add an adjustment factor for aircraft, weather, runway, and other conditions as well as experience, skill, ability and other pilot factors.

You will probably have to pre-calculate several data points at each stage, then interpolate the rest. For more exact plotting of data points, you will have to know the logarithmic or exponential algorithm used to calculate the curve in each step. Or, was each step drawn from observed data. Try Googling deriving logarithms.

Programs like ForeFlight has done this for several aircraft models.

Answer 3

I have done this before. It was a combination of FORTRAN for the numbers and Tcl/Tk for the plotting. How did it work?

First, you need a trim routine which computes the forces in all three axes and interprets the remainder as an acceleration. This requires an aerodynamic model and an engine model which could be represented by tables or discrete equations, as you like. Now you will have values which feed an integration where the conditions are updated for small time steps. Rinse and repeat with a time step of 0.5 to 2 seconds.

At some point the ground speed has reached v$_{rot}$ and your numeric model has to add negative elevator deflection to lift the nose. I used a standard pitch rate of 5° per second, but maybe you want to use less. Here the time step should be reduced for improved accuracy. If lift exceeds weight, the aircraft lifts off the runway and you have the distance and time for the ground run. Now the aircraft flies and climb rate needs to be chosen such that the aircraft arrives at the obstacle height at both 1.3 times v$_{Stall}$ and the obstacle height (might be 35 or 50 ft, depending on takeoff rules). Here you get the values for the full takeoff-length and time.

How would you get the climb rate right? I simply compared the projected time until obstacle height is reached and until 1.3 times v$_{Stall}$ is reached and adjusted the flight path angle such that both became equal.

Now you need to vary all the parameters of interest and repeat the calculation for variations in:

• ambient temperature
• take-off mass
• flap setting
• runway inclination
• wind

and whatever else comes to mind. For a landing chart you reverse the sequence but the approach is pretty much the same.