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- lostinspace2011
- Topic Author

Given 3000ft at +20C I managed to get the expected result of 4000ft

However for the remaining two questions I was not able to reproduce the answers provided in the book.

Using my calculator:

1500ft at +40C I ended up with around 7000ft

5000ft at +20C gave me around 4000ft

Could it be that the answers have been swapped around?

Using pen & paper:

1500ft at +40C

ISA Temp: 15-1.5x2=12C

ISA Deviation: 40-12=28C

Density Height=1500+28x120=1500+3360=4860ft

5000ft at +20C

ISA Temp: 15-5x2=5C

ISA Deviation: 20-5=15C

Density Height=5000+15x120=5000+1800=6800ft

So it looks like I don't know how to consistently use by CR3 ? Any pointers on where I am going wrong ?

However for the remaining two questions I was not able to reproduce the answers provided in the book.

Using my calculator:

1500ft at +40C I ended up with around 7000ft

5000ft at +20C gave me around 4000ft

Could it be that the answers have been swapped around?

Using pen & paper:

1500ft at +40C

ISA Temp: 15-1.5x2=12C

ISA Deviation: 40-12=28C

Density Height=1500+28x120=1500+3360=4860ft

5000ft at +20C

ISA Temp: 15-5x2=5C

ISA Deviation: 20-5=15C

Density Height=5000+15x120=5000+1800=6800ft

So it looks like I don't know how to consistently use by CR3 ? Any pointers on where I am going wrong ?

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- lostinspace2011
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- bobtait
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Yes, that's a common problem. You wouldn't blame anyone for using a window labeled 'TRUE ALTITUDE' to solve a problem relating to density altitude. However, the correct window to use is the one labeled 'TRUE AIR SPEED'. You use the AIR SPEED window to calculate density altitude. Not logical is it?

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- John.Heddles
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- ATPL/consulting aero engineer

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Unless the thinking process turns it around a bit ... going from IAS (strictly EAS, but let's not fuss too much) to TAS involves density (in the form of the square root of the density ratio - sigma). That, then, links the density (height) and speed.

In the ISA, sigma is defined for each (density) altitude, hence the prayer wheel's nomenclature.

Engineering specialist in aircraft performance and weight control.

Last Edit: 1 year 9 months ago by John.Heddles.

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- Carello
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Thanks John

I've always known that EAS/CAS and TAS were linked by the sqrt (inverse sigma), but I never twigged how the E6B (whiz wheel) did the conversion until now. Your post was a light bulb moment.

The conversion is quite simple once you realise that after setting PA and Temp in the airspeed window, the sqrt (inverse sigma) appears above the inner wheel index "10". From there it is a straight multiplication of EAS/CAS on the inner scale to get TAS on the outer scale.

Sorry to digress from the topic.

I've always known that EAS/CAS and TAS were linked by the sqrt (inverse sigma), but I never twigged how the E6B (whiz wheel) did the conversion until now. Your post was a light bulb moment.

The conversion is quite simple once you realise that after setting PA and Temp in the airspeed window, the sqrt (inverse sigma) appears above the inner wheel index "10". From there it is a straight multiplication of EAS/CAS on the inner scale to get TAS on the outer scale.

Sorry to digress from the topic.

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- John.Heddles
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- ATPL/consulting aero engineer

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A lot of folks get up tight about the wheels (whichever style - Dalton or CR [and there are others which have fallen out of use] - you might use).

Like so many activities, if one only learns the process as a mechanical Step A, Step B sort of thing it is extremely easy to forget how to use the device unless it is being used very frequently. Always, although you can manage without knowing the workings, it helps understanding if you do have a feel for how the device works. This, I fear, is one of the main problems with the advent of the super automatic aeroplanes of today where the pilot is trained largely on a reactive basis. In the extreme, this can result in disaster where none was necessary, such as AF 447.

It is useful to keep in mind that this side of the calculator starts off being a basic slide rule gadget with CD scales. These scales just do multiplication and division using standard logarithm addition and subtraction. (Don't fuss about that if you haven't heard those terms before .. very much nice to know stuff only).

The various cutouts are used, in essence, as lookup tables to set a number on one of the outer CD scales to be used in such multiplication and division activities.

If anyone has a desire for delving further, you can delve away to your heart's content here - www.sliderulemuseum.com/SR_Scales.htm

Engineering specialist in aircraft performance and weight control.

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