# Computing Speed by Weight



## Zipper730 (Jul 29, 2019)

I know, as a general rule if the plane's weight remains constant: You can compute horsepower via the difference in horsepower cube rooted. How do you manage to compute changes in weight?


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## pbehn (Jul 30, 2019)

Zipper730 said:


> I know, as a general rule if the plane's weight remains constant: You can compute horsepower via the difference in horsepower cube rooted. How do you manage to compute changes in weight?


Why do you want to?


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## Shortround6 (Jul 30, 2019)

Zipper730 said:


> I know, as a general rule if the plane's weight remains constant: You can compute horsepower via the difference in horsepower cube rooted. How do you manage to compute changes in weight?



I don't believe there is an easy formula. 

For weight alone (and not extra gun ports/ejection slots, radio aerials and other items that produce drag) the only difference/s are going to be induced drag and/or a slight change in the incidence of the wing. Since each wing is different (different size, shape and airfoil) the change in drag of fraction of a degree in incidence (attack angle) is not going to be consistent enough to reduce to a simple formula.
The next problem is that lift varies with square of the speed. adding 200lbs to a 6,000lb 350mph airplane is going to make a lot less difference than adding 200lbs to a 6000lb 175mph airplane since the change in incidence (attack angle ) of the wing is going to be a lot less for the faster plane and the change in drag is going to be lot less. 

For a given speed and weight there is going to be only one angle of incidence that gives level flight. Lower the angle and you descend, increase the angle and you climb.

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## swampyankee (Jul 30, 2019)

Subsonic aircraft (all piston-prop aircraft are subsonic) drag is lift due to drag and parasitic drag. It's usually approximated by




where A is aspect ratio, e is spanwise efficiency (usually about 0.8 for a monoplane) C_sub{d_sub(0)) is zero-lift drag coefficient (usually 0.022 to 0.025 for WW2-era monoplane fighters; the Mustang was about 0.017; the Bf109, about 0.029). A five percent increase in weight means a five percent increase in lift coefficient _at the same speed_. Power is



Usually, propellers are about 80 to 85% efficient in cruise. 

A better explanation is a http://www.dept.aoe.vt.edu/~lutze/AOE3104/levelflightperf.pdf


So, to a first approximation, at a constant speed, a 1% increase in weight requires a 2% increase in power.

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## pbehn (Jul 30, 2019)

The weight of an aircraft is a nominal value. At maximum speed a Spitfire is using about 120 gallons per hour of fuel I believe about 2 gallons of oil and when you fire the guns the weight changes by the second.


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## Zipper730 (Jul 30, 2019)

pbehn said:


> Why do you want to?


I wanted to basically figure out for the same aircraft, how it would perform if the weight changed with the same horsepower. The idea was to see the effects of speed with weight changes.


swampyankee said:


> A better explanation is a http://www.dept.aoe.vt.edu/~lutze/AOE3104/levelflightperf.pdf


This looks like a good link.


> So, to a first approximation, at a constant speed, a 1% increase in weight requires a 2% increase in power.


And every 1% loss of weight would require 2% less power to hold the same speed? Would that mean speed would go up 0.5% for every 1% decrease in weight or would I just use the cube rule?


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## pbehn (Jul 30, 2019)

Zipper730 said:


> I wanted to basically figure out for the same aircraft, how it would perform if the weight changed with the same horsepower. The idea was to see the effects of speed with weight changes.


Put the equations into a spreadsheet with a range of weights to produce a graph.

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## swampyankee (Jul 30, 2019)

Zipper730 said:


> And every 1% loss of weight would require 2% less power to hold the same speed? Would that mean speed would go up 0.5% for every 1% decrease in weight or would I just use the cube rule?



That would hold for a small range of weight changes.

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## Shortround6 (Jul 30, 2019)

Something doesn't seem right.

It may be me trying to deal with math over my head (way over) but that math doesn't seem to agree with real world results for the P-51 Mustang??

or for some airliners? 






adding weight inside (lead ballast or internal fuel tanks) does nothing to increase parasite drag. It only increases induced drag. Since induced drag drops with increased speed one formula would seem to have difficulty accounting for it??

Increasing the weight would have a much impact on stalling speed and climb?

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## pbehn (Jul 31, 2019)

Shortround6 said:


> Increasing the weight would have a much impact on stalling speed and climb?


And altitude.


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## Zipper730 (Nov 15, 2019)

Okay, I've probably clarified that math isn't my strong suit, plus I'm not even in math mode.

Looking at the link I was provided
T = Thrust
D = Drag
L = Lift
W = Weight
V = Velocity

I assume M is mass...

what's h, and δ (I know it's a lower case delta)...

I think η = propeller efficiency?


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## pbehn (Nov 15, 2019)

Zipper730 said:


> Okay, I've probably clarified that math isn't my strong suit, plus I'm not even in math mode.
> 
> 
> what's h, and δ (I know it's a lower case delta)...
> ...


in which equation?


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## Zipper730 (Nov 15, 2019)

pbehn said:


> in which equation?


All of 'em would be nice, but

Thrust Required
D = D(h*V*W)
D = D(h*M*W)

Thrust Available
T = T(h*v*δ)
T = T(h*M*δ)

would be a start


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## pbehn (Nov 15, 2019)

Zipper730 said:


> All of 'em would be nice, but
> 
> Thrust Required
> D = D(h*V*W)
> ...


They are not equations unless the values in brackets always result in an answer of 1. Where are they from, on this thread? in mathematics and physics "δ " or delta means the difference commonly used in calculus δ Y/δ X is the difference in Y divided by the difference in X and gives the gradient of a curve or line. What about "h"?


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## Zipper730 (Nov 16, 2019)

pbehn said:


> They are not equations unless the values in brackets always result in an answer of 1. Where are they from, on this thread?


The link in Reply #6


> in mathematics and physics "δ " or delta means the difference commonly used in calculus


Like Delta V. I figured because it was a capital delta, it had a different meaning (that might sound stupid, but)


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## pbehn (Nov 16, 2019)

Zipper730 said:


> The link in Reply #6
> Like Delta V. I figured because it was a capital delta, it had a different meaning (that might sound stupid, but)


It does, just google it.

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## Zipper730 (Nov 16, 2019)

I believe you -- I just didn't connect the dots at the time.


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## michael rauls (Nov 16, 2019)

Shortround6 said:


> Something doesn't seem right.
> 
> It may be me trying to deal with math over my head (way over) but that math doesn't seem to agree with real world results for the P-51 Mustang??
> 
> ...


Love that chart. Makes the relationship between the different types of drag easy to visualize.


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## Zipper730 (Nov 20, 2019)

I'm looking at the chart and things are starting to make a little sense: I guess my mind's been a bit cloudy over the past few days.


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## Zipper730 (Nov 27, 2019)

swampyankee said:


> Subsonic aircraft (all piston-prop aircraft are subsonic) drag is lift due to drag and parasitic drag. It's usually approximated by
> View attachment 546957
> where A is aspect ratio, e is spanwise efficiency (usually about 0.8 for a monoplane) C_sub{d_sub(0)) is zero-lift drag coefficient (usually 0.022 to 0.025 for WW2-era monoplane fighters; the Mustang was about 0.017; the Bf109, about 0.029). A five percent increase in weight means a five percent increase in lift coefficient _at the same speed_. Power is
> View attachment 546958
> Usually, propellers are about 80 to 85% efficient in cruise.


Being that I already know how to compute aspect ratio (one of the few things I do know how to compute), I'm curious if there are any tables that include spanwise efficiency, zero-lift drag coefficient?


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## Zipper730 (Jan 25, 2020)

Honestly, I think this link here: http://www.peninsulasilentflyers.co...rs.com/files/documents/Tom_Hunt_prop_info.pdf, is way easier to grasp than the previous link listed. I'm not sure if I grasp pitch in terms of inches as I don't know how degrees for rotation calculates out to inches -- when I think of degrees, I think of it in degrees.

That said: Static propeller thrust, if this formula works right would be
0.00000000000283 * rpm^2 * Prop Diameter^4 * Air Density/29.92

I'm not sure what density I should use in this case... there's several units of measure one could use.


S
 Shortround6
, 
W
 wuzak
, 
X
 XBe02Drvr


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## Zipper730 (Jun 9, 2021)

drgondog


Are there any tables that include spanwise efficiency or zero lift drag coefficients for WWII aircraft designs?


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## drgondog (Jun 10, 2021)

Zipper730 said:


> drgondog
> 
> 
> Are there any tables that include spanwise efficiency or zero lift drag coefficients for WWII aircraft designs?


There are many but none that I know of save two (an NACA and RAF table) with more than 10 or 12. All CDo related and most scale model wind tunnel values


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