Computing Speed by Weight

[Zipper730]

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?

 

[pbehn]

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?

 

[Shortround6]

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.

 

[swampyankee]

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.

 

[pbehn]

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.

 

[Zipper730]

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.

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?

 

[pbehn]

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.

 

[swampyankee]

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.

 

[Shortround6]

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?

 

[pbehn]

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

And altitude.

 

[Zipper730]

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?

 

[pbehn]

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)...

I think η = propeller efficiency?

in which equation?

 

[Zipper730]

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

 

[pbehn]

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

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"?

 

[Zipper730]

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)

 

[pbehn]

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.

 

[Zipper730]

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

 

[michael rauls]

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?

View attachment 546995

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?

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

 

[Zipper730]

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.

 

[Zipper730]

Subsonic aircraft (all piston-prop aircraft are subsonic) drag is lift due to drag and parasitic drag. It's usually approximated by View attachment 546957where 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 546958Usually, 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?