Rate of Climb and Climb Gradient Question
 

First post…

I have been given some rate of climb and climb gradient data and am having difficulty calculating the true airspeed used. I would really appreciate some advice on where I am going wrong.

Example data @ ISA and sea level
Gross Climb Gradient = 0.2014
Rate of Climb = 2,590 ft/min or 25.57552 nm/hr

My solution
ROC = KTAS * sine(Gross Climb Gradient)
= KTAS * Gross Climb Gradient (sine dropped due to small angle approximation)

Leading to
KTAS = ROC / Gross Climb Gradient
= 25.57552 / 0.2014
= 126.988
~= 127

My problem lies with the known indicated airspeed, which is 125 KIAS. Can anyone point me to how 125 KIAS becomes 127 KIAS?

Edit: Never mind, I see its at ISA/sea level.

2kts position error correction?

125 KIAS = 127 KEAS = 127 KTAS @ ISA Sea level

Climb gradient is vertical speed divided by ground speed, not TAS,
so wind could account for the difference.

It's worth noting that your climb gradient is approximately 20% or 12 degrees. This is not really a "small angle" for trigonometric purposes. It would be ok for in-flight approximations, but not for a written exam.

2590fpm x 60 / 6076 = 25.576 kts vertical speed.

Inverse Tan (0.2014) = 11.387 degrees.

25.576 / sin(11.387) = 129.5 kTAS.

Possible errors, in decreasing order of significance:

Pressure error (also known as position error)
Trigonometric error by dropping the sine
Rounding error in calculation

For in-flight purposes, it might look something like this:

My airspeed (IAS or TAS will do at sea level) is 125kts.
My required climb gradient is just over 20%.
125 x 20 = 2500fpm.
I need to achieve just over 2500fpm.