Range calculation for Airbus A320 aircraft

[lowwwien]

Homework Statement

Hi to all,

the Task I struggle with, is the range calculation from an Airbus A320 with the Breguet Range Equation which is defined as:

Homework Equations

R = (cl/cd) * (V/(g*SFC)) * ln(w0/w1)
with

• V = velocity
• g = gravity
• SFC = specific fuel consumption
• w0 = start weight
• w1 = end weight

For my following calculation I assumed the flight condition in cruise at 36000 ft, V = 230 m/s, Fuel of 10000 kg, w0 = 68000 kg, w1 = 58000 kg and L/D = 15

The SFC for the engine (CFM-56-5A1) of an Airbus A320-200 has an SFC of 0,596 lb/(lbf*hr) which is converted into kg/(N*s) with the divsion of 3600 to an SFC = 0,000165555555 kg/(N*s)

The Attempt at a Solution

This would lead to the following numbers in the breguet equation:

R = (15) * (230 / (9,80665*0,000165555555)) * 0,15906 = 338031,844 meters = 338 Kilometers

Did I bring in a mistake anywhere in my calculation? I think with one decimal more the result would be very realistic with 3380 km range for 10000kg fuel.

I'm very uncertain with the unit change for the SFC. Could this be the Problem?

Thank you very much in advance.

 

[Orodruin]

The SFC for the engine (CFM-56-5A1) of an Airbus A320-200 has an SFC of 0,596 lb/(lbf*hr) which is converted into kg/(N*s) with the divsion of 3600 to an SFC = 0,https://www.physicsforums.com/tel:000165555555 kg/(N*s

This is not correct. 1 lbf is the gravitational force exerted on a mass of 1 lb. In other words, g * 1 lb/lbf = 1.

I'm very uncertain with the unit change for the SFC. Could this be the Problem?

In other words: Yes.

 

[lowwwien]

This is not correct. 1 lbf is the gravitational force exerted on a mass of 1 lb. In other words, g * 1 lb/lbf = 1.In other words: Yes.

So the multiplication g*SFC is incorrect? And the equation should look like R = (cl/cd) * (V/(SFC)) * ln(w0/w1) ?

 

[Orodruin]

So the multiplication g*SFC is incorrect? And the equation should look like R = (cl/cd) * (V/(SFC)) * ln(w0/w1) ?

No. The unit conversion is wrong. However, if you multiply the g into SFC, you get the numerical value you obtained for SFC (but with units 1/s).

 

[Orodruin]

Also, whenever you are unsure about a unit conversion, I find the best thing to do is to double check with Wolfram Alpha or Google.

 

[lowwwien]

No. The unit conversion is wrong. However, if you multiply the g into SFC, you get the numerical value you obtained for SFC (but with units 1/s).

Ok, Thanks!
I guess I found the right conversion:

TSFC = (0.596lb)/(lbf⋅h) = ((0.596lb)/(lbf⋅h))⋅(4.448N/lbf)⋅((0.4536kg/lbm)^(−1))⋅((3600s/h)^(−1)) * (9,81m/s^2) = 0,0001655555555 1/s

Can you confirm that this would be the right result of the conversion?

 

[Orodruin]

Now your ingoing and outgoing quantities do not even have the same dimension ... lb and lbf are units of mass and force, respectively.

 

[lowwwien]

But the weight of 1 lb is 1 lbf right? So the ingoing is in fact 1/h and then converted into 1/s.
Test: I get the same result, if I divide 0,596 / 3600

 

[Orodruin]

But the weight of 1 lb is 1 lbf right?

Yes. In standard gravity. 1 lbf = 1 lb * g.

So the ingoing is in fact 1/h and then converted into 1/s.

No. Again, lbf and lb are units of different physical dimension.

 

[lowwwien]

"As a guy who has been working with these unit all my life, I can tell you that 1 lbm/hr is the same as 0.4536 kg/hr. The weight of this is (0.4546)(9.8)=4.448 N/hr. And we know that 1 lbf=4.448 N. So, to convert from imperial to metric in this case, all you need to do is divide by 3600" quote from Mr. Chestmiller Post #24 of Homework Help: Unit conversion:lbm/lbf*h to (N/s)/N

Right, lbf and lb are different Units. But now I'm confused if I can use the method from Mr. Chestmiller to receive the correct result.

 

[Orodruin]

As a guy who has been working with these unit all my life, I can tell you that 1 lbm/hr is the same as 0.4536 kg/hr. The weight of this is (0.4546)(9.8)=4.448 N/hr. And we know that 1 lbf=4.448 N. So, to convert from imperial to metric in this case, all you need to do is divide by 3600" quote from Mr. Chestmiller Post #24 of Homework Help: Unit conversion:lbm/lbf*h to (N/s)/N

Please include links if you are going to quote other threads.

 

[lowwwien]

2

Please include links if you are going to quote other threads.

https://www.physicsforums.com/threads/unit-conversion-lbm-lbf-h-to-n-s-n.928377/page-2

 

[Orodruin]

Did you read the rest of that thread? And no, you cannot just divide by 3600 to go from hours to seconds. You need to take care of the conversion from lb/lbf to kg/N. This is a dimensionful quantity.

Edit: Also note that the title of that thread makes no sense either. You cannot convert lb/(lbf h) to (N/s)/N. Different physical dimensions.

 

[lowwwien]

I did read all posts.

First to convert lb/lbf to kg/N I would muliply my starting value 0,596 by 0,4535 (lb to kg) and divide it by 4,448 (lbf to N).
What I need is end unit of kg/N*s so I would divide everything with 3600.

I need a value of meters at the end of the range equation so now:
-I mulitply the result from above by the g-force and receive a end unit of 1/s
-velocity/(1/s) = m

 

[Orodruin]

First to convert lb/lbf to kg/N I would muliply my starting value 0,596 by 0,4535 (lb to kg) and divide it by 4,448 (lbf to N).
What I need is end unit of kg/N*s so I would divide everything with 3600.

This is not equivalent to just dividing everything by 3600.

 

[lowwwien]

Do you know how the conversion should be done? I honestly don't know how I should proceed to get the proper value and unit out of the conversion.

 

[Orodruin]

Do you know how the conversion should be done?

Yes.

You described a valid procedure in #14. It is not equivalent to just dividing by 3600. But the better way of doing things is to keep g algebraic. 1 lbf = g * 1 lb so 1 lb/lbf = 1/g. What happens if you use this fact in your expression for SFC?

Edit: i.e., 0.596 (lb/lbf)/hr = ...