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True Airspeed solved...Now C-130 IAS at altitude

 
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Gene Whitt
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PostPosted: Fri Mar 25, 2005 4:22 am    Post subject: True Airspeed solved...Now C-130 IAS at altitude Reply with quote



Anyway, onto business. I do want to put a new twist
to the question :

This time, I am given TAS, Temp and Altitude. What is
the mathematical equation to solve for CAS? Again,
using our whiz wheel, we use this function every time
we fly because prior to our aircraft leveling off, we
compute an IAS which we give to the pilot so he's got
something to speed the plane up to once he reaches the
destination flight level.

Our whiz-wheel process is as follows: Our C-130's
normally fly 280 KTAS. During our climb, several
thousand feet prior to our level off, we check our
outside air temperature, correct the value for heat of
compression, then derive the temp at altitude using
the standard lapse rate. Given our level off
altitude, our predicted temperature, and our desired
TAS, we spin to determine the EAS which then gets
converted to CAS, then to IAS which I relay to my
pilot for him to fly.

As you already know, there's so many numbers to sort
through, and the formulas I've been getting from other
folks have not been much help because many do not use
the only values I can work with: temp, TAS, and alt.
Could you enlist your other Nav comrade to help me
crack this code?

Here's what I'm stuck on:

TAS = 1 / square-root of "rho" where "rho" is the
density ratio. Of course, where do I insert my given
values of temp and altitude in this?!? I further try
to break down the values of rho, but still to no
avail. And once I do, my ultimate challenge is to
flip everything around by isolating CAS in the
equation since that is what I was solving for.

Okay hopefully my rambling hasn't confused you too
much. But I'm sure you see where I'm going with this.
Again, thanks in advance for your help. I'll be sure
to tell some of our guys I've got some pro's trying to
crack this code!

Very Respectfully,
Archie

R.C. "Archie" DeJesus
Capt - USAF




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BTIZ
Guest





PostPosted: Fri Mar 25, 2005 6:04 am    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Reply with quote



Gene... I did not think that was all that tough.. but maybe I am missing
something here.. my old CR-2 which is packed.. had compressibility factor
built into the "whiz wheel"..

With my current E6B, if I know the "predicted" temperature in degrees C and
at my desired Pressure Altitude, I set that on one of the inner windows, I
can then read the Density Altitude... but with the Temp and Press Alt set
up.. the inner ring becomes CAS and the outer ring is TAS...

For example, setting 15C at sea level, TAS=CAS
I have the mini EA6B-1, so it is harder to read on these old eyes.
Setting -20C at 20,000ft, CAS (inner ring) reads 152 to equal 210KTAS
(an extreme value but shows the example)

Compressibility for a C-130 speed cannot be all that great... I was not a
C-130 nav... (read nave)... I flew B-1s, the Air Data Computer gave us a TAS
readout.. and also the pilot had a GS readout.. off our "my" INS.. when it
got critical.. I'd directed the ground speed I needed.

Maybe the Capt should get a copy of AFPAM 11-216, it replaced my AFM 51-50

It can be found on the web at
http://www.e-publishing.af.mil/pubfiles/af/11/afpam11-216/afpam11-216.pdf
and is a 69MB download.

BT

"Gene Whitt" <gwhitt (AT) ix (DOT) netcom.com> wrote

Quote:
Anyway, onto business. I do want to put a new twist
to the question :

This time, I am given TAS, Temp and Altitude. What is
the mathematical equation to solve for CAS? Again,
using our whiz wheel, we use this function every time
we fly because prior to our aircraft leveling off, we
compute an IAS which we give to the pilot so he's got
something to speed the plane up to once he reaches the
destination flight level.

Our whiz-wheel process is as follows: Our C-130's
normally fly 280 KTAS. During our climb, several
thousand feet prior to our level off, we check our
outside air temperature, correct the value for heat of
compression, then derive the temp at altitude using
the standard lapse rate. Given our level off
altitude, our predicted temperature, and our desired
TAS, we spin to determine the EAS which then gets
converted to CAS, then to IAS which I relay to my
pilot for him to fly.

As you already know, there's so many numbers to sort
through, and the formulas I've been getting from other
folks have not been much help because many do not use
the only values I can work with: temp, TAS, and alt.
Could you enlist your other Nav comrade to help me
crack this code?

Here's what I'm stuck on:

TAS = 1 / square-root of "rho" where "rho" is the
density ratio. Of course, where do I insert my given
values of temp and altitude in this?!? I further try
to break down the values of rho, but still to no
avail. And once I do, my ultimate challenge is to
flip everything around by isolating CAS in the
equation since that is what I was solving for.

Okay hopefully my rambling hasn't confused you too
much. But I'm sure you see where I'm going with this.
Again, thanks in advance for your help. I'll be sure
to tell some of our guys I've got some pro's trying to
crack this code!

Very Respectfully,
Archie

R.C. "Archie" DeJesus
Capt - USAF




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d&tm
Guest





PostPosted: Fri Mar 25, 2005 7:02 am    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Reply with quote


"Gene Whitt" <gwhitt (AT) ix (DOT) netcom.com> wrote

Quote:
Anyway, onto business. I do want to put a new twist
to the question :

This time, I am given TAS, Temp and Altitude. What is
the mathematical equation to solve for CAS? Again,
using our whiz wheel, we use this function every time
we fly because prior to our aircraft leveling off, we
compute an IAS which we give to the pilot so he's got
something to speed the plane up to once he reaches the
destination flight level.

Our whiz-wheel process is as follows: Our C-130's
normally fly 280 KTAS. During our climb, several
thousand feet prior to our level off, we check our
outside air temperature, correct the value for heat of
compression, then derive the temp at altitude using
the standard lapse rate. Given our level off
altitude, our predicted temperature, and our desired
TAS, we spin to determine the EAS which then gets
converted to CAS, then to IAS which I relay to my
pilot for him to fly.

As you already know, there's so many numbers to sort
through, and the formulas I've been getting from other
folks have not been much help because many do not use
the only values I can work with: temp, TAS, and alt.
Could you enlist your other Nav comrade to help me
crack this code?

Here's what I'm stuck on:

TAS = 1 / square-root of "rho" where "rho" is the
density ratio. Of course, where do I insert my given
values of temp and altitude in this?!? I further try
to break down the values of rho, but still to no
avail. And once I do, my ultimate challenge is to
flip everything around by isolating CAS in the
equation since that is what I was solving for.

Okay hopefully my rambling hasn't confused you too
much. But I'm sure you see where I'm going with this.
Again, thanks in advance for your help. I'll be sure
to tell some of our guys I've got some pro's trying to
crack this code!

as from my previous post

TAS=IAS*SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

IAS should have actually read CAS

just rearrange

CAS=TAS / SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

as before t = temp in C
PA= pressure altitude
the numbers in the square brackets is the breakdown of rhosl/rho
this equation doesnt allow for compressability which I dont think should be
significant at 280kt
Terry




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d&tm
Guest





PostPosted: Fri Mar 25, 2005 8:23 am    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Take 2 Reply with quote


"d&tm" <tfmann (AT) iprimusREMOVEME (DOT) com.au> wrote

Quote:

as from my previous post
TAS=IAS*SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

IAS should have actually read CAS

just rearrange

CAS=TAS / SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

as before t = temp in C
PA= pressure altitude
the numbers in the square brackets is the breakdown of rhosl/rho
this equation doesnt allow for compressability which I dont think should
be
significant at 280kt



The heart of this problem is having an equation for the pressure at a given
pressure height. The equation I used previously works well up to 10,000ft
( I aint never been higher than this in my warrior) . but a C130 would be
flying a bit higher, lets say up to 40,000 ft .
ISA pressure for altitudes up to 100,000 ft are given in this link
http://142.26.194.131/aerodynamics1/Appendix/ISA_Table.html

To turn this into a algebraic equation, plotting the data in excel and using
the fit trendline function works well. Up to 40,000 ft a quadratic gives an
excellent fit to the data

( if you want to go up to 100,000 ft then a 3 rd order polynomial is a
better fit)
but back to our quadratic

the best fit line is

Pressure =3.439E-5 *PA^2-3.406*PA +100678

Pressure is in units of Pa
PA = pressure altitude in ft

getting density from pressure and temp is just the gas equation

rho =PM/RT

rho = kg /m^3
P = Pa
M= .029 kg ( molecular weight of air)
R=8.31
T= temp K ( Celcius +273.15)

then substitute P for the quadratic equation used above

rho =(3.439E-5 *PA^2-3.406*PA +100678) *.029 / (8.31*(T+273.15)

then CAS = TAS /SQRT[1.225/((3.439E-5 *PA^2-3.406*PA +100678) *.029 /
(8.31*(T+273.15))]

(1.225 was the density of air at sea level)
Terry
student pilot and commercial calculator operator




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d&tm
Guest





PostPosted: Fri Mar 25, 2005 9:09 am    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Take3 Reply with quote


"d&tm" <tfmann (AT) iprimusREMOVEME (DOT) com.au> wrote

Quote:

"d&tm" <tfmann (AT) iprimusREMOVEME (DOT) com.au> wrote in message
news:4243b875$1_1 (AT) news (DOT) iprimus.com.au...

as from my previous post
TAS=IAS*SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

IAS should have actually read CAS

just rearrange

CAS=TAS / SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

as before t = temp in C
PA= pressure altitude
the numbers in the square brackets is the breakdown of rhosl/rho
this equation doesnt allow for compressability which I dont think should
be
significant at 280kt



The heart of this problem is having an equation for the pressure at a
given
pressure height. The equation I used previously works well up to 10,000ft
( I aint never been higher than this in my warrior) . but a C130 would be
flying a bit higher, lets say up to 40,000 ft .
ISA pressure for altitudes up to 100,000 ft are given in this link
http://142.26.194.131/aerodynamics1/Appendix/ISA_Table.html

To turn this into a algebraic equation, plotting the data in excel and
using
the fit trendline function works well. Up to 40,000 ft a quadratic gives
an
excellent fit to the data

( if you want to go up to 100,000 ft then a 3 rd order polynomial is a
better fit)
but back to our quadratic

the best fit line is

Pressure =3.439E-5 *PA^2-3.406*PA +100678

Pressure is in units of Pa
PA = pressure altitude in ft

getting density from pressure and temp is just the gas equation

rho =PM/RT

rho = kg /m^3
P = Pa
M= .029 kg ( molecular weight of air)
R=8.31
T= temp K ( Celcius +273.15)

then substitute P for the quadratic equation used above

rho =(3.439E-5 *PA^2-3.406*PA +100678) *.029 / (8.31*(T+273.15)

then CAS = TAS /SQRT[1.225/((3.439E-5 *PA^2-3.406*PA +100678) *.029 /
(8.31*(T+273.15))]

(1.225 was the density of air at sea level)

I take back what I said about the compressability error, Looking up a chart

of compressibility error vs altitude and speed at 280 kts and 30,000ft the
error was about 15 kts.
OK so now we do need a compressability correction , stay tuned!



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d&tm
Guest





PostPosted: Fri Mar 25, 2005 9:08 pm    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Reply with quote


"Gene Whitt" <gwhitt (AT) ix (DOT) netcom.com> wrote

Quote:
Anyway, onto business. I do want to put a new twist
to the question :

This time, I am given TAS, Temp and Altitude. What is
the mathematical equation to solve for CAS? Again,
using our whiz wheel, we use this function every time
we fly because prior to our aircraft leveling off, we
compute an IAS which we give to the pilot so he's got
something to speed the plane up to once he reaches the
destination flight level.

Gene , have you seen this Willaims site (link below) , it is the most

comprehensive list of aviation equations I have seen, it covers all of this
stuff, including the compressibility errors, and it is all in a format you
can plug straigt into excel or a programmable calculator.
http://williams.best.vwh.net/avform.htm#Mach
Man , I will have some fun with this stuff. I.m gunna start with working
out the Mach No of my warrior!
Terry



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BTIZ
Guest





PostPosted: Sat Mar 26, 2005 2:46 am    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Reply with quote

he wants to do it on an E6B in flight... not on a PDA

BT

"d&tm" <tfmann (AT) iprimusREMOVEME (DOT) com.au> wrote

Quote:

"Gene Whitt" <gwhitt (AT) ix (DOT) netcom.com> wrote in message
news:XlM0e.3962$H06.1569 (AT) newsread3 (DOT) news.pas.earthlink.net...
Anyway, onto business. I do want to put a new twist
to the question :

This time, I am given TAS, Temp and Altitude. What is
the mathematical equation to solve for CAS? Again,
using our whiz wheel, we use this function every time
we fly because prior to our aircraft leveling off, we
compute an IAS which we give to the pilot so he's got
something to speed the plane up to once he reaches the
destination flight level.

Our whiz-wheel process is as follows: Our C-130's
normally fly 280 KTAS. During our climb, several
thousand feet prior to our level off, we check our
outside air temperature, correct the value for heat of
compression, then derive the temp at altitude using
the standard lapse rate. Given our level off
altitude, our predicted temperature, and our desired
TAS, we spin to determine the EAS which then gets
converted to CAS, then to IAS which I relay to my
pilot for him to fly.

As you already know, there's so many numbers to sort
through, and the formulas I've been getting from other
folks have not been much help because many do not use
the only values I can work with: temp, TAS, and alt.
Could you enlist your other Nav comrade to help me
crack this code?

Here's what I'm stuck on:

TAS = 1 / square-root of "rho" where "rho" is the
density ratio. Of course, where do I insert my given
values of temp and altitude in this?!? I further try
to break down the values of rho, but still to no
avail. And once I do, my ultimate challenge is to
flip everything around by isolating CAS in the
equation since that is what I was solving for.

Okay hopefully my rambling hasn't confused you too
much. But I'm sure you see where I'm going with this.
Again, thanks in advance for your help. I'll be sure
to tell some of our guys I've got some pro's trying to
crack this code!

as from my previous post
TAS=IAS*SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

IAS should have actually read CAS

just rearrange

CAS=TAS / SQRT[((1.228 *8.31*(T +273)) / {(100404-3.0863*PA)*0.029))]

as before t = temp in C
PA= pressure altitude
the numbers in the square brackets is the breakdown of rhosl/rho
this equation doesnt allow for compressability which I dont think should
be
significant at 280kt
Terry






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d&tm
Guest





PostPosted: Sat Mar 26, 2005 6:25 am    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Reply with quote


"BTIZ" <btiznospm2 (AT) cox (DOT) nospm.net> wrote

Quote:
he wants to do it on an E6B in flight... not on a PDA

whats an E6B ?



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BTIZ
Guest





PostPosted: Sat Mar 26, 2005 3:27 pm    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Reply with quote

a circular slide rule, marked for aviation purposes.. with 60 as a base
instead of 10, for computing time.. as in time required to fly a set
distance at a set speed.. ahh... but I see you are from Auzzieland.. same
idea as the Jeppeson CR1 and CR2 "whizzwheels"

http://www.lightandflight.com/merchant2/merchant.mvc?Screen=CTGY&Store_Code=pilot&Category_Code=FC


BT

"d&tm" <tfmann (AT) iprimusREMOVEME (DOT) com.au> wrote

Quote:

"BTIZ" <btiznospm2 (AT) cox (DOT) nospm.net> wrote in message
news:c241e.296$ZV5.0 (AT) fed1read05 (DOT) ..
he wants to do it on an E6B in flight... not on a PDA

whats an E6B ?





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d&tm
Guest





PostPosted: Sat Mar 26, 2005 8:36 pm    Post subject: Re: True Airspeed solved...Now C-130 IAS at altitude Reply with quote

My reading of the post was that the good captain was looking for a
mathematical equation, which I assumed he would plug into an electronic
calculator , plam pilot or flight computer of some type. But anyways now I
know what an E6B is , thanks

Terry

"BTIZ" <btiznospm2 (AT) cox (DOT) nospm.net> wrote

Quote:
a circular slide rule, marked for aviation purposes.. with 60 as a base
instead of 10, for computing time.. as in time required to fly a set
distance at a set speed.. ahh... but I see you are from Auzzieland.. same
idea as the Jeppeson CR1 and CR2 "whizzwheels"


http://www.lightandflight.com/merchant2/merchant.mvc?Screen=CTGY&Store_Code=

pilot&Category_Code=FC
Quote:


BT

"d&tm" <tfmann (AT) iprimusREMOVEME (DOT) com.au> wrote in message
news:424500c4$1_1 (AT) news (DOT) iprimus.com.au...

"BTIZ" <btiznospm2 (AT) cox (DOT) nospm.net> wrote in message
news:c241e.296$ZV5.0 (AT) fed1read05 (DOT) ..
he wants to do it on an E6B in flight... not on a PDA

whats an E6B ?







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