incubus
Posts: 74
Joined: Thu Apr 26, 2001 9:48 pm

Airspeed V Groundspeed

Is there a formula that is used to calculate equivalent groundspeed from airspeed at a given altitude? I am trying to explain to someone that it is possible for indicated airspeed to reduce with altitude whilst equivalent ground speed increases (is this right, I think so.)

And are there any extraneous variables, such as air density, that will affect this?

broke
Posts: 1299
Joined: Wed Apr 24, 2002 8:04 pm

RE: Airspeed V Groundspeed

Indicated airspeed is pretty close at sea level, but it gets an increasing error with altitude due to the reduction in air density and, in part, to the installation on the airplane. I used to be pretty good at calculating my true airspeed using the E-6B circular calculator (I still have mine). With the advent of Air Data Computer (ADC) Systems, this problem, for first Air Transport Aircraft and later corporate airplane, went away. Now a lot of the higher scale general aviation airplanes have some type of ADC. This error results in an airspeed reading that is lower than the actual airspeed. When you are comparing groundspeed to airspeed, you seem to be assuming a no wind condition; which is good place to start to simplify the calculation but rarely, if ever, happens in real life.
One of the interesting points about a simple airspeed indicator is that an airplane's indicated stall speed will pretty much remain the same at any altitude. Of course, at altitude, the true airspeed at stall is higher.

goboeing
Posts: 2450
Joined: Mon Jun 05, 2000 5:31 am

RE: Airspeed V Groundspeed

See if these sound about right:
Altitude Conversion Factor

0 1.00
5000 1.08
10000 1.17
15000 1.26
20000 1.37
25000 1.50
30000 1.64
35000 1.79
40000 2.02

So just muliply your indicated airspeed by the conversion factor for the closest altitude.

Nick

erasmus
Posts: 256
Joined: Thu Jun 07, 2007 11:46 pm

RE: Airspeed V Groundspeed

TAS=IAS + FL/2

is a good approximation.
TAS = True airspeed
IAS = Indicated Airspeed
FL= Flight Level

So at FL210 (21000 ft), if your IAS=250 kts your TAS= 250+210/2= 365 Knots
(You spoke about groundspeed, well groundspeed=TAS in calm wind conditions.)

If you want a more scientific explanation, you have to download this.

Regards,
Erasmus

Guest

RE: Airspeed V Groundspeed

The term airspeed to me is not specific enough to answer your question correctly. The relationship between True Airspeed and Ground speed is pretty simple...after you resolve the direction part of the vectors, Ground speed is simply True airspeed plus tail wind, magnitude-wise.

There are formulas and tricks to convert between indicated airspeed to equivalent airspeed and true airspeed ...I can get into this a bit more if you would like but I feel you already know these.

Best Regards,
Nut

Guest

RE: Airspeed V Groundspeed

Dear Incubus:
Sure, you can work with mathematic formulas or graphs to convert from one to another unit... as mentioned in other postings...
Even in this day and age I still sometimes refer to a "pilot slide rule" which you can buy in the UK for probably some 20 pounds sterling...
The "E6-B" type is probably the most popular but it is generally designed more for lower altitudes and speeds... conversion for airliner jet speeds and flight level cannot always be obtained on E6-Bs...
One very popular "slide rule" is the Jeppesen CR-3 type, has all low altitude, low speed or high level and high speed conversions capabilities...
In UK and Europe, the "Aristo" slide rules are high quality and very accurate, unfortunately very expensive...
Learning to use such a slide rule takes a few days of practice with the little instruction manual provided... many things you can do with these slide rules... I even use mine when going shopping in UK or Europe to convert currencies!
(s) Skipper

FredT
Posts: 2166
Joined: Thu Feb 07, 2002 9:51 pm

RE: Airspeed V Groundspeed

IAS (EAS)/TAS = ambient pressure at altitude / ambient pressure at the airspeed indicators calibration pressure (i e SLS pressure).

Cheers,
Fred
I thought I was doing good trying to avoid those airport hotels... and look at me now.

bio15
Posts: 1048
Joined: Fri Mar 23, 2001 8:10 am

RE: Airspeed V Groundspeed

Yes Incubus, you can have a lower IAS at high flight levels that represents a much faster speed than if you had the same IAS at sea level. The conversion I have heard of is based on an approximation that states that IAS drops by 0.02 every 1000 feet.

Therefore, if you are at FL390 and the indicated airspeed (IAS) shows 240:

39 x 0.02 = 0.78

IAS has dropped a 78 percent. Therefore your true airspeed is:

240 + (240 x 0.78) = 427 knots

At sea level, the indication would most certainly be 427 IAS.
(Remember it is an approximation)

Hope it helps a bit since most was already answered by the knowledgeable ones!

-bio

Guest

RE: Airspeed V Groundspeed

Incubus...
Just add 2% per thousand feet to your IAS airspeed for an approximate TAS. It's not dead on, but it's close enough for the girls that my wife will let me date.

Jetguy

incubus
Posts: 74
Joined: Thu Apr 26, 2001 9:48 pm

RE: Airspeed V Groundspeed

Thanks everyone, I think there's enough here to help me explain this properly, and I now understand it better myself.

PW4084
Posts: 287
Joined: Tue Mar 06, 2001 7:31 pm

RE: Airspeed V Groundspeed

To use an E6-B for compressibility problems you can purchase a slide such as this one if your current model doesn't have an 'f' factor conversion chart:

https://www.avshop.com/catalog/product.html?productid=2239&categoryid=29

If you've looked at the conversion table, you'll see that the compressibility factor is 1.0 at or below 10,000 feet up to 250 KCAS. The opposite extreme is 550 KCAS @ 50,000' PA-- .84.

So with a CAS of 550 Knots, the Equivalent Airspeed is 550(.84) 462.

Now add true air temp and you can find TAS.

Jetguy, cool conversion, I've always used Indicated + (1/2 Flight Level P.A.)=Quick and Dirty TAS (and I mean capital Q/D  ) I.E. 250 KIAS @ FL240 = 370 KTAS. And of course this disregards EAS so when I'm flying my F-104 Starfighter X-country I'll have to employ more precision.

Regards, PW4084

Guest

RE: Airspeed V Groundspeed

Dear PW4084...
Honestly I prefer Jeppesen CR-3 or Felsenthal PT to the old E6-B...
The CR-3 offers computations up to Mach 1.8 and is the one that I see most often in the hands of my fellow crewmembers... The Felsenthal PT offers solutions up to Mach 3.5... but I dont fly a Concorde or a SR-71... I kept my old Air Force issue CPU 26A/P, an E6-B type "whiz-wheel" as a souvenir... not too accurate, and the only thing I love about that old thing, it is in metal, I have owned a few plastic CR-3s which melted in the sun rays on the glareshield... they looked like a melted pancake after being ignored a few minutes on top of the glareshield...
Ray Lahr, an ex-UAL captain designed the original CR-3... I once met him, some 25 years ago, and he told me how the E6-B was erroneous to compare to his masterpiece... well, at least he got a copyright on his design, and probably is rich nowadays... this is just trivia... Happy landings -
(s) Skipper

PW4084
Posts: 287
Joined: Tue Mar 06, 2001 7:31 pm

RE: Airspeed V Groundspeed

B747skipper,

Thanks for the info, I've been a CR-3 fan for a while also. According to Jeppesen, 140 degrees F, is the magic number where the CR-3 becomes nothing more than a melted drink coaster. I've also got a CPU 26A/P and when I'm really bored I'll run problems and compare answers between the two. I've seen that the CR-3 has a US Navy inventory number, I wonder if they use it to teach pilots or navigators. That's cool that you had the chance to meet Mr. Lahr.
Best Regards, PW4084

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