jetflyer
Posts: 603
Joined: Sat Aug 08, 2009 7:38 am

Calculation Of Rate Of Climb

Wed Mar 22, 2006 8:30 am

Hi, I have a project underway to calculate the rates of climb of airliners based on various factual information about the airfoil.

This includes calculating the lift quantity and induced drag in pounds. Thew following data will go into a spreadsheet, you see, and these are the requirements:

The input example below is of a generic aircraft.

INPUT
AIRFOIL

Wing Area: 980sq/ft
Mean Chord: 11.06ft
Wing Span: 88.6ft
Aspect Ratio: 8.01
Camber - %C: 4.05
Thickness - %crd: 9.25

OUTPUT REQUIRED

Total lift at a given airspeed (lbs) at sea level
Induced drag at a given airspeed (lbs) at sea level

AIRCRAFT INPUT

Gross takeoff weight: 107,456lbs
Gross Thrust: 25,120lbs
Parasite Drag

OUTPUT desired:

Some form of calculation that gives me the rate of climb based on the excess thrust/lift taking into account drag levels and aircraft weight.

Is this asking too much maybe? I know there are many "experts" in this area on the board, so I'd be happy to know a way of calculating these parameters to give me some intelligible data on Microsoft Excel.

That aircraft above is an example, with most of the data required to calculate this stuff, can anyone show me the formulas to create the lift/drag quantity and work out the rate of climb?
 
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zeke
Posts: 10095
Joined: Thu Dec 14, 2006 1:42 pm

RE: Calculation Of Rate Of Climb

Wed Mar 22, 2006 10:42 am

We are addicted to our thoughts. We cannot change anything if we cannot change our thinking – Santosh Kalwar
 
jetflyer
Posts: 603
Joined: Sat Aug 08, 2009 7:38 am

RE: Calculation Of Rate Of Climb

Wed Mar 22, 2006 7:48 pm

Thanks, I've been using that site as reference, but if only calculates the climb angle, for my aircraft I calculated that with 10,000lbs of excess thrust and a weight of 107456lbs the climb angle equals 5.33 degrees approximately. However, that doesn't tell me much, because it could be anything from 1fpm to 5,000fpm.

I was told once that in order to climb the amount of excess thrust and lift in pounds put together had to exceed the aircraft's weight. Therefore I need to use those properties of the wing above to work out the rate it would climb at a 5.33 degree climb angle, based on a given airspeed and and a certain quota of lift based on aspect ratio, wing loading etc... There must be a way!
 
David L
Posts: 8552
Joined: Tue May 18, 1999 2:26 am

RE: Calculation Of Rate Of Climb

Wed Mar 22, 2006 8:43 pm

Quoting Jetflyer (Reply 2):
Therefore I need to use those properties of the wing above to work out the rate it would climb at a 5.33 degree climb angle, based on a given airspeed

I'm not sure I follow. Are you saying the climb angle or the angle of attack (or something else) is 5.33o? If it's the angle at which the aircraft climbs and you have a given speed, wouldn't simple trigonometry give you the rate of climb?

Of course, as usual, I may be missing something.  Smile
 
vikkyvik
Posts: 11907
Joined: Thu Jul 31, 2003 1:58 pm

RE: Calculation Of Rate Of Climb

Wed Mar 22, 2006 9:17 pm

I think what you're missing is the property of the airfoil. Yes, chord, thickness, etc. are the physical properties, but to know the lift, you need to know the plot of lift coefficient vs. angle of attack. Once the lift coefficient is determined, you can calculate the total lift, and therefore, the induced drag. I don't believe you can calculate the lift just with the figures you gave, because you don't know what the incidence angle of the wing is in the first place.

Unfortunately, many modern commercial airplanes tend not to use one airfoil over the whole wingspan. The airfoil will change as you go from fuselage to wingtip.

God, it's been about 3 years since I went over this stuff, but if you need the formula for the lift or induced drag (both for a given lift coefficient), then I can supply those.

~Vik
I'm watching Jeopardy. The category is worst Madonna songs. "This one from 1987 is terrible".
 
David L
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Joined: Tue May 18, 1999 2:26 am

RE: Calculation Of Rate Of Climb

Wed Mar 22, 2006 9:29 pm

Yes, it's the "5.33o climb angle" that's confusing me. What exactly is "climb angle"?
 
jetflyer
Posts: 603
Joined: Sat Aug 08, 2009 7:38 am

RE: Calculation Of Rate Of Climb

Wed Mar 22, 2006 10:38 pm

Quoting David L (Reply 3):

I'm not sure I follow. Are you saying the climb angle or the angle of attack (or something else) is 5.33o? If it's the angle at which the aircraft climbs and you have a given speed, wouldn't simple trigonometry give you the rate of climb?

No, you add the angle of attack to the angle of climb (5.33*) to get the attitude, but the point is that the angle of attack depends on the airspeed, which in turn affects the drag quantity which allowed me to calculate excess thrust in the first place.

The angle of climb is trigonometry it is implie that if the aircraft had excess thrust to match its weight it would climb straight up, but because its excess thrust is only a fraction of its weight, it climbs at a certain angle depending on that amount.

However, it doesn't tell me the lift produced by the airfoil.

The calculation of the climb angle was sin-1(10000/107456) = 5.339748767 degrees.

How do I go about determining the lift co-efficient? I used the NASA foil simulator to create the wing to those specifications, and it shows a lift calculation in pounds and a co-efficient. But I'm wondering how it calculates them.

[Edited 2006-03-22 14:42:16]
 
David L
Posts: 8552
Joined: Tue May 18, 1999 2:26 am

RE: Calculation Of Rate Of Climb

Wed Mar 22, 2006 10:52 pm

Quoting Jetflyer (Reply 6):

OK. I'm crawling back into my box now!
 
A3204eva
Posts: 1041
Joined: Wed Feb 18, 2004 4:25 am

RE: Calculation Of Rate Of Climb

Thu Mar 23, 2006 6:14 am

Well for the standard 3º climb/descent path it's groundspeed x5 Big grin
"They have lady pilots......... they're not that good, but they have 'em"
 
Pihero
Posts: 4232
Joined: Mon Jan 31, 2005 5:11 am

RE: Calculation Of Rate Of Climb

Thu Mar 23, 2006 6:54 am

Jetflyer,
I don't think anybody on this site could help you if he/she wasn't a manufacturer's performance engineer.
Vikkyvik started with a glimpse of some of the parameters you would need.
Basically, a polar of the complete aircraft would be desirable and in all my years I haven't been able to procure one. The wing polar in itself is not enough.
On the other hand, most posters here could provide you with the basic aerodynamic equations and the only way you could fill up that spreadsheet of yours would be to plot a lot of climb performance situations from an AOM, but it will only give you fleet average, not the accurate data you need.
The same remark is also valid for engine performance : For instance, what is the thrust value of engine X at OAT = 35°c ? I have no idea, I only know that I could expect N1=98%....and so on.

Sorry couldn't help you more
Contrail designer
 
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Jetlagged
Posts: 2562
Joined: Sun Jan 23, 2005 3:00 pm

RE: Calculation Of Rate Of Climb

Thu Mar 23, 2006 5:23 pm

If you aren't accelerating, and you have a climb angle gamma, then

Lift = Weight / cosine (gamma)

Not exact, but close enough for your purposes I would have thought.
The glass isn't half empty, or half full, it's twice as big as it needs to be.
 
Doktor
Posts: 29
Joined: Tue Mar 21, 2006 10:50 pm

RE: Calculation Of Rate Of Climb

Thu Mar 23, 2006 10:16 pm

Hi Jetflyer!
If you are really interessted I could send you an pdf file from my lecture notes of flight mechanics. You can definitly find your answers, but they are not that easy to understand...
Dok
 
jetflyer
Posts: 603
Joined: Sat Aug 08, 2009 7:38 am

RE: Calculation Of Rate Of Climb

Thu Mar 23, 2006 11:50 pm

Hi there, that would be interesting, I'll send you my E-mail address, or actually, it should be on my profile.
 
Doktor
Posts: 29
Joined: Tue Mar 21, 2006 10:50 pm

RE: Calculation Of Rate Of Climb

Fri Mar 24, 2006 4:15 am

Jetflyer,
I tried to send you a mail, but I couldn attach anything. You got to send an instant message or mail me your address!
 
liedetectors
Posts: 323
Joined: Thu Jul 21, 2005 10:44 am

RE: Calculation Of Rate Of Climb

Fri Mar 24, 2006 8:21 am

Hey Jetflyer, Any college level flight mechanics text book should be able to help. I would look at mine and help you out, but they are all at work.
If it was said by us, then it must be true.

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