We’re about to go into far more detail about true altitude and true height than anyone probably needs to. But if you’re curious about the logic behind why we use the whiz wheel instead of a calculator for these questions, read on.

Calculating true altitude is something ATS students are generally pretty strong at, but across everyone sitting the ATPL Navigation exam, it continues to be an area people get wrong. In fact, true altitude and true height calculations are right at the top of the list of weak areas identified in CASA’s exam feedback.

I think at least part of the problem comes down to people using a less accurate method because, on the surface, it looks more precise.

At ATS, we only teach the whiz wheel method for true altitude and true height calculations. We do this because it’s simpler, it’s better suited to the type of information you’re normally given in the exam and, perhaps surprisingly, it’s actually more accurate.

The other method you’ll commonly see is the mathematical method. You might have learnt it from another theory provider, or picked it up from friends or coworkers. It uses the approximation of 4 ft per 1,000 ft per degree Celsius of temperature difference:

Correction = Height × Temperature Difference × 0.004

This may blow your mind, but this method is actually less accurate than using your whiz wheel, for more than one reason.

If you’re already sticking to the whiz wheel method, perfect. You don’t really need to read any further.

If you still need some convincing, let’s look at the maths behind it.

First Problem: 0.004 Isn’t Actually a Constant

The 0.004 figure makes the calculation nice and easy.

If we’re 10°C away from the reference temperature and have a height of 10,000 ft:

10,000 × 10 × 0.004 = 400 ft

Easy.

But there’s a problem: 0.004 isn’t an exact atmospheric constant.

The relationship we’re trying to approximate depends on absolute temperature (temp meassured from absolute zero). That means we need to think about temperature in Kelvin, rather than simply degrees Celsius.

For example:

  • +40°C = approximately 313 K
  • +15°C = approximately 288 K
  • −25°C = approximately 248 K

A simplified way of seeing the problem is to look at the reciprocal of absolute temperature.

At +40°C:

1 / 313 ≈ 0.00319

At +15°C:

1 / 288 ≈ 0.00347

At −25°C:

1 / 248 ≈ 0.00403

See the problem?

At around −25°C (unheard of in Australia), our 0.004 approximation happens to be very close.

At +40°C (pretty common), however, the equivalent figure is closer to 0.0032.

Yet the calculation method blindly uses 0.004 in both cases.

So although your calculator might give you a beautifully precise answer to the nearest foot, the number you’ve put into it was an approximation in the first place.

Second Problem: The Relationship Isn’t Linear

There’s another issue with the calculation method.

It assumes a basically linear relationship:

4 ft × thousands of feet × degrees of temperature difference

But the real atmospheric relationship isn’t perfectly linear.

Again, thinking in Kelvin makes this easier to see.

Consider two temperature changes of exactly 10°C (same as 10 K).

Going from:

300 K → 290 K

is a change of:

10 / 300 = 3.33%

But:

250 K → 240 K

is a change of:

10 / 250 = 4.00%

Both temperatures changed by exactly 10°C, but they’re not the same proportional change in absolute temperature.

That’s important because the thickness of a pressure layer is related to absolute temperature.

The 0.004 method takes a relationship that changes with temperature and simplifies it into a nice linear rule.

That’s useful for a quick approximation if you’re in a plane needing it in a hurry.

It’s not necessarily the best method if we’re trying to get the most accurate answer for an exam.

But Surely a Calculator Is More Accurate Than Reading a Whiz Wheel?

This is probably where the misconception comes from.

Imagine your calculator gives you:

9,637 ft

You then use your whiz wheel and read something around:

9,600 ft

It’s very tempting to think:

“Well, 9,637 must be more accurate. I’ve calculated it exactly.”

You haven’t.

You’ve calculated an approximation very precisely.

That’s an important distinction.

Precision and accuracy aren’t the same thing.

The fact that your calculator displays an answer to the nearest foot doesn’t mean the atmospheric model behind that answer is accurate to the nearest foot.

The true-altitude scales on the whiz wheel better represent the atmospheric relationship rather than relying on the fixed 0.004 approximation.

So yes, there is potential for some small reading error involved in physically reading the wheel, but the underlying method is more accurate.

The Whiz Wheel Also Suits CASA Questions Better

There’s another reason we use the whiz wheel at ATS: it’s better suited to the questions you’re actually going to get.

The 0.004 calculation works nicely when someone hands you an ISA deviation.

But CASA doesn’t necessarily make life that convenient.

You’re more often than not given something like a surface temperature (like one from an ATIS), along with the relevant altitude information, rather than simply being told “ISA −12°C”.

That means if you want to use the mathematical method, you first need to manipulate the information in the question into the form required by your formula.

With the whiz wheel, the information provided in the question is much more naturally suited to the method.

It’s therefore not just more accurate. In our view, it’s also easier and faster in the exam.

If you’re preparing for the Navigation exam, you can read more about the subject and our course here: ATPL Navigation (ANAV) Course.

Most Importantly, We Want to Match CASA’s Answer

There’s one final practical consideration.

CASA’s expected answers are calculated using the whiz wheel method, so that’s the method we want our students using as well.

Even if you perform the 0.004 calculation perfectly, the simplified nature of the formula means you can end up with an answer slightly different from the answer CASA expects.

And in a type in (or even multi choice) question, that’s what ultimately matters.

You don’t get extra marks because your working was mathematically consistent with an approximation. You need to select the answer CASA has calculated.

That’s another major reason we teach the whiz wheel method: we want to calculate true altitude the same way CASA is calculating the expected answer.

Let’s Look at an Actual Example

Here’s a good example of why all of this actually matters in the exam.

In this question, the aircraft is overhead an aerodrome at 5,600 ft indicated, the aerodrome elevation is 558 ft, QNH is 1021 hPa, and the surface temperature is a very warm +39°C.

The acceptable answer range is:

5,982 ft to 6,082 ft True Altitude

Let’s use the mathematical method.

First, we calculate the pressure altitude at the aerodrome:

558 + [(1013 − 1021) × 30] = 318 ft

Then, we calculate the indicated height above the aerodrome:

5,600 − 558 = 5,042 ft

At 318 ft pressure altitude, the standard ISA temperature is approximately:

+14.37°C

Our actual surface temperature is +39°C, so our temperature deviation is approximately:

ISA +24.63°C

Now we apply the commonly taught 0.004 correction:

True Height = 5,042 × [1 + (0.004 × 24.63)]

That gives us a true height of approximately:

5,539 ft

Add the aerodrome elevation back on:

5,539 + 558 = 6,097 ft True Altitude

There’s just one problem.

6,097 ft is outside the acceptable range.

The upper limit is 6,082 ft, meaning we’ve ended up approximately 15 ft outside tolerance, despite correctly applying the mathematical method.

Now solve exactly the same question using the whiz wheel and you’ll end up smack bang in the middle of the acceptable answer range.

And that’s where this stops being just an interesting discussion about atmospheric theory.

At a relatively high temperature of +39°C, the shortcomings of the fixed 0.004 approximation have become large enough to actually put our answer outside the tolerance of the question.

There was nothing wrong with the arithmetic.

The error came from the approximation itself.

That’s exactly why at ATS we teach the whiz wheel for true altitude and true height calculations.

It’s simpler, better suited to the information you’re normally given, more accurate and, most importantly, it gives us the best chance of arriving at the same answer CASA does.

So if you’re already using the whiz wheel for your true altitude calculations, keep doing exactly that.