# Range calculation for Airbus A320 aircraft

• lowwwien
In summary, the conversation discusses the use of the Breguet Range Equation to calculate the range of an Airbus A320, using various inputs such as velocity, fuel, weight, and specific fuel consumption (SFC). There is some confusion about the unit conversion for SFC, but it is ultimately determined that the correct conversion is 0.000165555555 kg/(N*s). The conversation also touches on the conversion between imperial and metric units, and the importance of considering physical dimensions when doing unit conversions.
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.

Last edited:
lowwwien said:
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.

lowwwien said:
I'm very uncertain with the unit change for the SFC. Could this be the Problem?
In other words: Yes.

berkeman
Orodruin said:
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) ?

lowwwien said:
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).

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.

Orodruin said:
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?

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

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

lowwwien said:
But the weight of 1 lb is 1 lbf right?
Yes. In standard gravity. 1 lbf = 1 lb * g.

lowwwien said:
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.

"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.

lowwwien said:
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

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.

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

lowwwien said:
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.

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.

lowwwien said:
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 = ...

## 1. How is the range calculated for an Airbus A320 aircraft?

The range of an aircraft is calculated by taking into account several factors, including the type and amount of fuel on board, the aircraft's weight and load, weather conditions, and the type of flight plan. The Airbus A320 has a maximum range of approximately 3,300 nautical miles.

## 2. What is the maximum fuel capacity of an Airbus A320?

The maximum fuel capacity of an Airbus A320 is approximately 6,000 gallons. However, the actual amount of fuel loaded onto the aircraft for a specific flight may vary depending on the distance of the flight, the weight of the aircraft, and other factors.

## 3. How does the weight of the aircraft affect its range?

The weight of the aircraft has a significant impact on its range. A heavier aircraft will require more fuel to fly the same distance, which will decrease its range. Additionally, the weight of the aircraft also affects its performance and fuel efficiency, which can also impact its range.

## 4. What role do weather conditions play in calculating the range of an Airbus A320?

Weather conditions can have a significant impact on the range of an aircraft. Strong headwinds can decrease the aircraft's speed and increase fuel consumption, reducing its range. Similarly, strong tailwinds can increase the aircraft's speed and improve fuel efficiency, increasing its range.

## 5. Can the range of an Airbus A320 be extended?

The range of an aircraft can be extended by making modifications to the aircraft, such as installing additional fuel tanks or using more efficient engines. However, these modifications can be costly and may require recertification of the aircraft.

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