The question I originally posted is word for word the question I had in front of me.

The question, as stated, is a poor question as it does not provide adequate information to decide whether we are talking about a generic situation, in which case the answer would include wind, or the 20.7.4 WAT situation, in which case the answer would be figured for nil wind, like all WAT considerations. Indeed, if you work backwards from the answers, both solutions are there.

How do you get around the problem ? Beats me, you can only hazard a guess at what the question is looking for.

I just didn't think to correct TAS for altitude.

Tuck that one away for future reference.

So, I applied the ECHO and got 92 KT IAS TOSS. Looking at my whizz wheel that's 96 KT TAS.

You don't have any PEC data for the Echo so you don't have much choice other than to use IAS. However, you need to be aware that the correct calculation is EAS to TAS which, for light aircraft, is near enough to CAS to TAS. as the EAS compressibility correction is pretty well zero If you use IAS, you will attract an error unless the PEC at the speed for the configuration is zero.

Less the HW = 81 KT GS.

Refer to my earlier comments.

Relooking at the available answers.

a) 620 feet/min - bin
b) 580 feet/min - select if you run the WAT nil-wind sum
c) 290 feet/min - bin
d) 490 feet/min - select if you run the generic sum accounting for wind
e) 460 feet/min - bin

Noticing @Bosi72's answer above, I do wonder whether the simply multiplying by the % is sufficiently accurate rather than what I did.

You have set up a convoluted equation but, no matter, that's OK.

If you run the sum, accounting for the unit conversions, the "correct" answer will vary from the short cut approximate answer by a tad over 1 %. In the scheme of things, not worth too much worrying about.

Following on from an offline query regarding units, it may be useful if folk have the standard unit conversion sequence in the back of their minds.

The sum can be set up either using TAS or GS, in which case the equation is

tan (grade) = ROC/GS, or

sin (grade) = ROC/TAS

You should be aware that, for small angles,

sin (gradient angle) ~ tan (gradient angle) ~ gradient angle

so we can use the following approximations

grade ~ ROC/GS, or

grade ~ ROC/TAS

Now, to run the unit conversions - grade is a number without units, but we have ROC (ft/min) and a speed (nm/hr) on the other side so the sum doesn't work out properly. To fix this, we just convert the RHS units to other units so that we can cancel units out in the same sort of way we cancel numbers out in a quotient. So, using the first equation

grade = ROC/GS,

we can use the algebraic idea that multiplying by unity ("1") doesn't change the value of an equation.

Now, if we note that ROC is in ft/min and GS is in kt (nm/hr)

and that 6076 ft = 1 nm, 60 min = 1 hr, we can fiddle a bit with the equation

grade = ROC/GS ft/min / nm/hr x 1 nm/6076 ft x 60 min/1 hr

cancel the various units out in the usual fashion (eg where there is "ft" on the top and the bottom, they cancel out and so on for the remaining units) and we end up with

grade = ROC/GS x 60/6076

where grade is a number. If we want it to be a percentage we need to multiply both sides by 100%/1 to get

grade % = ROC/GS x 6000/6076

which is

grade % = ROC/GS x 0.987

so the error comes down to around 1.3 % if we do the usual pilot sum. We can live with that sort of approximation.

The examiner will be looking for the approximate answer.