# ATP Written - convert Mach number to TAS

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**1**Gets Weekends Off

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Joined APC: Nov 2008

Posts: 229

**ATP Written - convert Mach number to TAS**

I'm studying for my ATP written and for the life of me I can't find an easy way to convert Mach number to TAS as is required for some of the flight plan calculations.

In my previous life I was an engineer so I know how to calculate it if I have the speed of sound at a given temperature. So I guess the question is there an easy way to calculate speed of sound at given temperatures?

The gleim book says the following :

Quote:
The problem is my E6B doesn't appear to have a Mach index probably becuase my E6B is the one I used for my private and not many 172's in GA use Mach number. I also have an electronic e6b I bought ages ago which will convert TAS to mach number but can't convert mach number back to TAS. Doh!

Refering to the old faithful Aerodynamics by Naval Aviators you get the following:

M=V/a

M=Mach number

V=TAS in kts

a=speed of sound in kts=ao(theta)**(1/2)

ao=speed of sound at standard see level (661kts)

theta=tempertature ratio T/To (temperatures in Kelvin)

btw **(1/2) is math speak for square root of theta as I couldn't be arsed working out how to put in a proper square root symbol.

So in the case of the gleim problem:

theta = T/To = (273-41)/(273+15) = .806

(theta)**(1/2) = .896

a = 661*.896 = 593.26kts

V = M*a = 593.26 * .78 = 462.8kts

Great I get the correct answer but there must be a quicker way .... anybody got the magic formula?

In my previous life I was an engineer so I know how to calculate it if I have the speed of sound at a given temperature. So I guess the question is there an easy way to calculate speed of sound at given temperatures?

The gleim book says the following :

To obtain TAS from .78 Mach, use the calculator side of your flight computer and set OAT at -41C over the Mach index. Find the Mach number on the "minutes" scale, and read TAS above on "miles" scale, or 463kts.

Refering to the old faithful Aerodynamics by Naval Aviators you get the following:

M=V/a

M=Mach number

V=TAS in kts

a=speed of sound in kts=ao(theta)**(1/2)

ao=speed of sound at standard see level (661kts)

theta=tempertature ratio T/To (temperatures in Kelvin)

btw **(1/2) is math speak for square root of theta as I couldn't be arsed working out how to put in a proper square root symbol.

So in the case of the gleim problem:

theta = T/To = (273-41)/(273+15) = .806

(theta)**(1/2) = .896

a = 661*.896 = 593.26kts

V = M*a = 593.26 * .78 = 462.8kts

Great I get the correct answer but there must be a quicker way .... anybody got the magic formula?

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**2**New Hire

Joined APC: Apr 2008

Posts: 7

On the E6B, look at the window under the temperature scale (+50 to -50) on the inner wheel. Rotate the wheel until the mach no. index appears in that window. It should line up with 85 on the outer scale.

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**3**Che Guevara

Joined APC: Aug 2005

Posts: 6,408

Who cares? They are both on the same gauge. I know that doesn't help you much but just shows how impracticable some of these questions are.

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**4**Line Holder

Joined APC: Feb 2009

Position: QB/@Lolitas/Baccara

Posts: 28

Approximate True Airspeed to Mach #.

Multiply the Mach number by 570.

This probably isn't exact enough for the test though.

Multiply the Mach number by 570.

This probably isn't exact enough for the test though.

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**5**Gets Weekends Off

Thread Starter

Joined APC: Nov 2008

Posts: 229

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**6**Gets Weekends Off

Joined APC: Jul 2005

Position: EMB120 CA

Posts: 299

For these I just used Sheppard Air's study aid. It used to be a free document on their website awhile back that it seems they took down, probably to sell their software. I still have my copy, and as of 1 year ago, worked just great. Basically just a little memorization of some numbers and tables, and you'll have all the answers to the performance/weight and balance that you need. Just supplement that with memorizing from the Gleim/ASA prep the answers to the non-figured questions, and that's all you need. Anyone can PM me for a copy of the study aid, worked wonders for me.

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**7**Furlough line holder

Joined APC: Jan 2007

Position: CRJ2, ATR, CRJ7, E145, 737

Posts: 1,845

oh my gawwwdddddddd

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**8**Chief Jeppesen Updater

Joined APC: Oct 2005

Position: Executive Transport Driver

Posts: 3,080

As a GENERAL rule of thumb, when taking the ATP written, if you can't figure out the correct answer, ALWAYS choose the answer with the middle value.

A - 176.8 lbs

B - 179.3 lbs

C - 177.4 lbs

Choose C.

A - 9200 feet

B - 8900 feet

C - 9400 feet

Choose A.

A - 176.8 lbs

B - 179.3 lbs

C - 177.4 lbs

Choose C.

A - 9200 feet

B - 8900 feet

C - 9400 feet

Choose A.

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**9**Gets Weekends Off

Joined APC: Aug 2005

Position: Reserve on tha Beach

Posts: 546

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**10**Gets Weekends Off

Joined APC: Aug 2007

Position: rear GV

Posts: 294

get an up to date book and memorize all the anwsers!!! That test is just another thing they can make you study for..

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