Airspeed/Mach/Ground Speed Conversion chart

[Essah]

I'm wondering if anyone is in possession of, or knows if it's possible to find a chart that shows the relation between airspeed, Mach and ground speed at various altitudes (Assuming level flight).

 

trying to wrap my head around it, but it seems very complex.

[bongodriver]

groundspeed will always be a factor of wind so you cannot have a fixed chart, if you assume still air then ground speed = TAS (true air speed)

 

IAS can be converted to TAS by roughly increasing by 2% per 1000'

 

at a constant indicated airspeed your true airspeed and mach number will increase with altitude.

 

Mach number will vary with temperature.

 

this google search brings up a ton of charts

 

https://www.google.co.uk/search?q=ias+tas+mach+chart&source=lnms&tbm=isch&sa=X&ei=5roEVMnjLIvgaLGjgpgP&ved=0CAcQ_AUoAg&biw=1920&bih=944#facrc=_&imgdii=_&imgrc=UgsylmnTM147EM%253A%3BEtutYFPVAwnuZM%3Bhttp%253A%252F%252Fi958.photobucket.com%252Falbums%252Fae65%252Fajv00987k%252FIasTasChart.jpg%3Bhttp%253A%252F%252Fforum.warthunder.com%252Findex.php%253F%252Ftopic%252F109074-a-crash-course-in-aerodynamics-and-physics%252F%3B999%3B451

Edited September 1, 2014 by bongodriver

[Random]

Get yourself an E6b "whiz wheel" flight computer or the electronic equivilant. Does thr IAS to TAS calculations along with a lot more too. A big help for navigating without needing to alt-tab and use online calculators or tables

[Flagrum]

Get yourself an E6b "whiz wheel" flight computer or the electronic equivilant. Does thr IAS to TAS calculations along with a lot more too. A big help for navigating without needing to alt-tab and use online calculators or tables

Printable paper E6B: http://ben.com/flying/e6b/

[Random]

Nice find!

[effte]

Let us turn this into a religious debate. I see your E6B and raise with a CR-3! :D

 

http://www.jeppesen.com/download/misc/crinstructions.pdf

 

Superior for Mach calculations, and easier to use on the fly in the cockpit. Less intuitive than the E6B, admittedly, but practise solves that!

[ericoh]

http://www.aviationexplorer.com/Virtual_E6B_Flight_Calculator_Emulator.html Edited September 1, 2014 by ericoh

[bongodriver]

Or just take my advice and increase the IAS by 2% for every 1000'

[effte]

Which still gives TAS, which is on an exclusive list of values not actually asked for?

[bongodriver]

Which still gives TAS, which is on an exclusive list of values not actually asked for?

 

To calculate ground speed one must know TAS

[aaron886]

Since no one has directly said it yet... an E6B or equivalent (online or whatever) will be easier than a chart, since these require multiple inputs and would be in graph/chart format (rather than table) in most cases.

[Emu]

I'm wondering if anyone is in possession of, or knows if it's possible to find a chart that shows the relation between airspeed, Mach and ground speed at various altitudes (Assuming level flight).

 

trying to wrap my head around it, but it seems very complex.

The speed of sound varies linearly with temperature, starting at 1224kph at SL and going to 1062kph at 11,000m. So you can use liner interpolation in between. Above 11,000m it is constant up to about 20,000m, which is as high as most things go.

 

IAS is basically what the indicator thinks airspeed is because it assumes it's still at ground level, where density is 1.225kg/m^3.

 

So in the equation:

 

Pt = Ps + 0.5.Density.Velocity^2

 

it assumes Density is 1.225kg/m^3 when calculating back from measured Pt and Ps, you get:

 

sqrt{[2.(Pt - Ps)]/Density}

 

So TAS/IAS = sqrt[1.225/Actual Density] [A]

 

Density varies non-linaerly:

 

https://en.wikipedia.org/wiki/File:StandardAtmosphere.png

 

Now:

 

If Po = Pressure at SL, then P at altitude is given by:

 

P/Ptropopause = exp{-gHt/RTtrop} = exp{-0.000158Ht}

 

where

 

Ptropopause = 22,700Pa, Ttrop = temp. at tropopause and Ht = height above tropopause (11,000m).

 

Below the tropopause (Tsl - temp. at sea level and Psl = pressure at sea level):

 

P = Psl.[1 - ([Gamma-1]/Gamma).(g.H/R.Tsl)]^(Gamma/[Gamma-1])

 

or taking Gamma as 1.4:

 

P = Psl.[1 - (0.2857).(g.H/R.Tsl)]^3.5 = Psl.[T/Tsl]^5.26 = Psl[1-(0.0000226 x H)]^5.26 = Psl.[1 - 0.00003388H]^3.5B

 

P/Density^1.4 = Constant, so

 

P/D^1.4 = Psl/Dsl^1.4, therefore:

 

D = [P/(Psl/Dsl^1.4)]^0.714

 

Put in B for:

 

D = [(Dsl^1.4).[1 - (0.2857).(g.H/R.Tsl)]^3.5]^0.714 = Dsl.[1 - (0.2857).(g.H/R.Tsl)]^2.5 Now put that back in [A]

 

TAS/IAS = sqrt[1.225/Actual Density] becomes:

 

TAS/IAS = sqrt{1/[1 - (0.2857).(g.H/R.Tsl)]^2.5}

 

So:

 

TAS = IAS.{1/[1 - (0.2857).(g.H/R.Tsl)]^1.25} = IAS.{1/[1 - 0.0003388H]^1.25} up to 11,000m

 

R = 287J/kg.K

g = 9.80665m/s^2

Tsl = 288.15

 

From B Ptropopause = 19,813Pa and P = exp{-gHt/RTtrop}.Ptropopause = exp{-0.000158Ht}.Ptropopause

 

P/D^1.4 = Psl/Dsl^1.4, therefore:

 

D = [P/(Ptrop/Dtrop^1.4)]^0.714 = [(Dtrop^1.4).exp{-gHt/RTtrop}]^0.714 = Dtrop.{[exp{-gHt/RTtrop}]^0.714}

 

TAS/IAS = sqrt[1.225/Actual Density] becomes: TAS/IAS = sqrt[1.225/(Dtrop.{[exp{-gHt/RTtrop}]^0.714)]

 

From [A] Dtrop = 0.381kg/m^3, hence: TAS/IAS = sqrt[3.215/([exp{-0.000158Ht}]^0.714)], so:

 

TAS = IAS.{1/[1 - (0.2857).(g.H/R.Tsl)]^1.25} = IAS.{1/sqrt[3.215/([exp{-0.000158Ht}]^0.714)]} above 11,000m

 

Ht = height above 11,000m (i.e. H - 11,000m)

Edited September 2, 2014 by Emu

[HiJack]

That should cover it :music_whistling:

[Emu]

I did actually make a mistake. I had TAS and IAS the wrong way round in the first equation.:lol:

 

Corrected.

 

I should point out that the above assumes standard atmospheric temperature variation. If this is not the case, you need to correct for this by using the difference between measured Ps and theoretical Ps at your given altitude. You also need to correct for wind if you wish to calculate ground speed. We will leave compressibility affects alone for now.

Edited September 2, 2014 by Emu

[ericoh]

Since it seems like we have an expert here allow me to throw in a question.

 

How does one calculate Dewpoint via Temperature (OAT) and Relative Humidity (%)?

 

And the other way, how is Relative Humidity (%) calculated via Dewpoint and Temperature (OAT)?

 

Couldnt realy find any good explanations.

 

:thumbup:

[Emu]

If relative humidity is 100%, then current temperature = dew point.

 

Increasing pressure while keeping temperature constant increases dew point.

 

Increasing temperature while keeping pressure constant reduces relative humidity.

 

RH = Relative Humidity = PpH20 / PsH20 where

 

Pp = Partial pressure of H20 and PsH20 = Saturated vapour pressure of H20

 

PsH20 = (1.0007 + 0.000346P).6.1121.exp([17.502T+4780.85]/[T+514.13])

 

P = Absolute pressure (Pa) and T = Dry Bulb Temperature of air (K)

 

Pp = (Vp + Ptot) / Vtot

 

Vp = Partial Volume of gas (m^3), Vtot = total volume of gas(m^3), Ptot = Total pressure of gas (Pa)

 

Tdp = 257.14X / (18.678 - X)

 

Where X = ln { (RH/100).exp[(17.67 - (OAT/234.5)).(OAT/(257.14+OAT))]}

 

A simple approximation is given by:

 

Tdp = OAT - [(100 - RH) / 5]

 

and RH = 100 - [5.(Tdp - OAT)]

 

OAT in degC.

 

Roughly due point falls by 1degC relative to air temperature for every 5% reduction in humidity. Of course there is the difference between wet bulb and dry bulb temperature to consider. Wet bulb OAT is usually less than dry bulb below 100% RH due to the cooling effect of evaporation but most aircraft temperature measurements will be ambient dry bulb temperature.

Edited September 3, 2014 by Emu

[ericoh]

Awesome, thanks alot Emu, this helped me!