True Ground Speed Formula

[Admin]

If we know that GS = TAS + Vw, i.e. true air speed plus wind.

 

However, GS changes drastically if I dive or climb which is obvious because I'm covering 0 ground distance if I dive vertically.

 

What is therefore a real GS formula from TAS? It has to take into account the wind (Vw) but also the "3D angle of the aircraft" (for the lack of better expression).

 

 

[kgwilson]

I have no idea what that formula is but my GPS is a pretty accurate indicator of my ground speed. The formula would have to take into account the wind plus angle from horizontal, a bit like determining the crosswind component on landing.

 

 

[mnewbery]

This answer is specific to single engine poston aircraft under 120 knots IAS. This is my opinion not canon law so please use best judgement.

 

Vertical part of the equation isn't considered for two reasons:

 

The climb or descent gradient is assumed to be 3% which is 500 Ft/minute at 100 knots or a bit less than 1/10th of a mile per minute or 6 knots vertically. So your climb speed at Vy of 75 knots indicated is more like 74 knots GS using pythagoras theorem at nil wind. Increase the climb rate to 1000ft/min and its more like 73 knots GS. This is less than the difference between the IAS and the CAS; and

 

The planned TAS and GS doesn't take climb or descent phases into account however if a long climb is anticipated it might make a few minutes difference which could be recovered depending in the GS during the descent

 

 

[VFR Pilot]

It's just distance divided by time, it doesn't need to be complicated or anything.

 

 

[kaz3g]

If we know that GS = TAS + Vw, i.e. true air speed plus wind./QUOTEOnly correct for level flight.

 

However, GS changes drastically if I dive or climb which is obvious because I'm covering 0 ground distance if I dive vertically./QUOTEGround speed will be zero in a vertical dive.

 

What is therefore a real GS formula from TAS? It has to take into account the wind (Vw) but also the "3D angle of the aircraft" (for the lack of better expression).

Horizontal distance divided by time = GS is the easy calculation

 

Otherwise you have to calculate the horizontal vector component from your dive or climb angle and add that to the wind. Vhoriz = Vdive x cos a but you still have to calculate the wind. Far too complicated.

 

Kaz

 

[Ryanm]

It's just distance divided by time, it doesn't need to be complicated or anything.

Agreed! Yes it’s interesting, but you can work it out based on DIST vs time and adjusting for wind.

 

 

[facthunter]

The extreme vertical dive will not really happen in the real world. When you are dealing in shallow angles the length of the 2 long sides of the triangle differs by very little. Whatever the COSINE for descent angle ( adjacent over hypotenuse) is, use the trig charts. and factor the TAS accordingly.. You will travel through the air more than your G/S would indicate as the slanted path is longer than the path viewed from directly above. At small angles of descent It's not much at all.. You planes L/D ratio will give you an approximate glide angle. Different speeds have different L/D ratios and if you use partial power it's a whole new ball game, .but the angle of the descent path is what we are dealing with, if I understand your question. . Nev