Mach number

[FsNovice]

I'm working on some new fuel calculator, but have hit a snag in my calculations. I know the mach number of the A320 at cruise is 0.78, but to be actually able to work out the number of hours in the air, and use my mph calculations to work out fuel needed for cruise based on numbers i have for fuel flow on it per hour. My problem is, how do i work out, on the cuff, for each calculation in my app, the mph at different Fl's if i know the mach number. Is this possible, or will each FL need to be coded with a different speed based on the mach number. Cheers, i'm sure on of you lot with superior understanding of these complex mathemathic statements can expain how this is done, or not as the case may be!!!

Cheers

Fsnovice

[Brett_Henderson]

A fuel calculator won't need to know airspeed; knots, mph or mach... doesn't matter.

All it cares about is fuel flow... and uses that information against the amount of fuel remaining to give a calculated endurance. What kind of range that might be, is a function of ground speed.. and that depends on the wind.

[Brett_Henderson]

Sooo.. at any given time, you'd need to know the TRUE airspeed (the difference between indicated, and true, airspeed changes with altitude)... and then calculate the ground speed according to the wind.

If you're doing this for something like a gauge... you can skip a step and retrieve ground-speed in the XML coding of the gauge.

[FsNovice]

But this is not to be used in sim, so i have no live flight data. I have the cruise speed (0.78) and the fuel used per hour.  Its not to calculate the fuel in the tanks at any given flight time, but the fuel needed to put into the virtual tanks before begginning a flight. If that makes sense.  So i need to convert speeds. Cheers

[beaky]

This is way out of my league as a pilot and certainly as a programmer, but I think you need to build your calculations around a performance chart for the aircraft concerned...a chart that includes verified flow for various FLs and power settings. It could work much as a slide rule would. Where you'd get that data for the plane I don't know...

[FsNovice]

Right, back to the drawing board it seems. Thanks brett and Rottydaddy for your help so far, much appreciated.

[C]

Where you'd get that data for the plane I don't know...

The Operators Manaul. Sadly I don't think they're available freely. A simple way would be with an online mach to IAS to TAS to GS etc conversion tool within which one could input altitude and temperature data. Sadly the only one I found searching earlier was rather unfriendly in that I had to work backwards, and it didn't offer GS or IAS either, so would require further corrections.

[Splinter562]

The calculation you want to do is not terribly complicated. But I don't think it will be giving you the information you are expecting. To clarify, the calculation you are using are:

endurance [ hr ] = fuel load [lb] / fuel flow [lb/hr]
range [NM] = ground speed [NM/hr] * endurance [ hr ]

Or you may want to go backwards and get fuel load required given a range and ground speed:

flight time [ hr ] = range [NM] / ground speed [NM/hr]
fuel load [lb] = fuel flow [lb/hr] * flight time [ hr ]

You issue is that you have airspeed in mach, and you want to get it in knots (or some other unit of velocity). To do that you need the following equation:

true air speed [NM/hr] = mach number [mach] * speed of sound [NM/hr]

The speed of sound in air varies with temperature, and temperature varies with altitude. So, you can go out and find the equations that describe temperature variation with altitude in the standard atmosphere then calculate the speed of sound... Or you can just look up a standard atmosphere table and hard code the values for each flight level. That will give a ballpark figure for fuel required.

There is another major factor that will influence range, the winds. Winds. At altitude, winds (especially in the jet stream), can make a huge difference in range. You'd probably want to make a field to add a headwind / tailwind component. To get ground speed (to use in the equations above) you'd use:

ground speed = true air speed + tailwind
or
ground speed = true air speed - headwind

That'll give you a more refined estimate of fuel required for the flight and is probably a good place for you to start. Be careful with this though, for jet engines, fuel flow varies greatly with altitude so using the fuel flow for the A320 at mach 0.78 and FL370 will not work for mach 0.78 and FL270.

Now, that being said, this type of calculation works great for small GA aircraft. The cruise performance rarely matches the numbers in the book so working anything beyond a ball park figure probably won't help you much. However, jets are a bit different, it is possible to get much more accurate fuel planning using the manufacturer's data. This data is usually a combination of engineering analysis and flight test data which allows you to build a fairly accurate fuel estimate and takes into account many important factors we have left off here. This includes fuel, time, and distance used to climb to altitude (which is fairly significant in a jet), cruise performance at a range of mach numbers and altitudes, and corrections for different weights and off-standard atmospheric conditions. This would require that you obtain the performance charts for the airplane you want and either do some curve fitting or generate tabular data for your calculator to use.

[C]

That'll give you a more refined estimate of fuel required for the flight and is probably a good place for you to start. Be careful with this though, for jet engines, fuel flow varies greatly with altitude so using the fuel flow for the A320 at mach 0.78 and FL370 will not work for mach 0.78 and FL270

Although certainly for sim use, and short haul trips I doubt the difference will be very much at all, certainly less than 1tonne (metric) between said levels - probably less than 0.5t. The big difference between levels will be the burn to get there - you may only use 2 or 3 tonnes to reach FL250, but nearer 4 or so to reach FL350 and above.

[Splinter562]

OK. Since we're starting to step a little deeper into jet engine performance. I think the best way to go is to show some actual data. I went into FSX and flew some test points in the default Boeing 737-800. I used the default payload and 50% fuel (23,000lbs). Through the magic of flight sim, all test points are at the same gross weight (132,000 lbs) and in standard atmosphere. Here are the results:


AltitudeIASTASFuel FlowRange
ftknotsknots1000 lb/hrNM
15,0001501875.61536
15,0002002486.01901
15,0002503077.61858
15,00030036310.21637

25,0001502205.61807
25,0002002916.02231
25,0002503587.62167
25,00030042110.81793

35,0001502625.62152
35,0002003446.02637
35,0002504208.02415
35,000300N/AN/AN/A


What does this all mean to jet aircraft range? Well, first thing to note is that, for the most part, engine fuel flow remains the same for a certain indicated airspeed regardless of altitude. So you can say that a certain indicated airspeed will require a certain fuel flow at any altitude. Here's the kicker, as altitude increases, the true airspeed that you get from a certain indicated airspeed goes up. So as you increase altitude, you get a higher true airspeed for the same indicated airspeed, and since fuel flow is about constant with indicated airspeed the result is: As you increase altitude, you get a higher true airspeed for the same fuel flow.

It's about as close as you'll get to getting something for nothing in the airplane world. That is why commercial air carriers will pop up to altitude, even on very short flights. The gains that you get by flying at the higher altitudes are usually greater than the fuel spent getting there.

[FsNovice]

Cheers splinter, that data is much appreciated, i will be digesting that over the next week or so, and working how i can incoropate said figures into my system.