# Homebuilt Aircraft Formulas

### Help Support HomeBuiltAirplanes.com:

##### Well-Known Member
I am curious to know if anyone knows the formula for scaling aircraft weight and airspeed.

IE if I want to make a scale replica of a full scale aircraft, how do I calculate a scaled down weight and airspeed.
Darrol Stinton's two books* as well as being very good design and flight test references also cover in a lot of detail the issues of scale replica aircraft.

*Design Of The Aeroplane
Flying Qualities and Flight Testing of the Airplane

#### Christian Moreton

##### Active Member
Darrol Stinton's two books* as well as being very good design and flight test references also cover in a lot of detail the issues of scale replica aircraft.

*Design Of The Aeroplane
Flying Qualities and Flight Testing of the Airplane
Ok, sure, I'd love to order books, wait weeks, and pour through the books. But I was hoping that somebody could just tell me the formula.

##### Well-Known Member
The behavior is very non linear, there is no simple formula! Scale effects on structure are different to handling etc etc

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#### Turd Ferguson

##### Well-Known Member
Pie are squared.......that's all the formulas you need to know ! ! !

#### Turd Ferguson

##### Well-Known Member
LOL. Just reminded me In the first movie Rise of the Phoenix.
Heinrich Dorfmann was a riot.

#### Topaz

##### Super Moderator
Staff member
Log Member
Unfortunately, we seem to have lost the OP. @Osnel , if you're reading this, I hope you'll come back and keep learning. I see no reason you can't design an ultralight like Peter, and the forum would be happy to help you on your path to doing so.

##### Well-Known Member
Lift = time+money
I thought it was Lift = Time * Money Squared? Or am I confusing it with the motorsport speed formula??

#### BJC

##### Well-Known Member
HBA Supporter
Unfortunately, we seem to have lost the OP.
Permission to drift, Sir?

If I had to write just one formula to start with, it would be F = d(mv) / dt.

What would others be?

BJC

#### Aerowerx

##### Well-Known Member
If I had to write just one formula to start with, it would be F = d(mv) / dt.
The conventional form of this is F=ma, which is also F=m*dv/dt

And if you include the loss of mass by burning fuel, your version is correct.

#### BJC

##### Well-Known Member
HBA Supporter
The conventional form of this is F=ma, which is also F=m*dv/dt

And if you include the loss of mass by burning fuel, your version is correct.
The special case, simplified, form is F = ma.

The general version is as I wrote it.

BJC

#### wsimpso1

##### Super Moderator
Staff member
Log Member
Ok, sure, I'd love to order books, wait weeks, and pour through the books. But I was hoping that somebody could just tell me the formula.
Christian Moreton,

If you do not like the advice given on here, you do not have to take it. In particular, simply dumping a little math without underlying theory may take one down an undesired path. The background information is usually important.

No one here is required to help you at all. Those that do are volunteering their time and hard earned knowledge to provide you with the references they think you need given your questions. Reply with sarcasm and anger, and you may find their help to you will cease.

In addition, use of the advanced search function may show you that almost all topics have been talked about before, with references, basic knowledge, experience, etc all contributed and discussed. Using searches may find you threads and posts on your exact topic that you may then read, take lessons from, and then contribute to.

Billski

#### 12notes

##### Well-Known Member
Log Member
I wrote a program for calculating costs. Here's the source code for the main loop:

While(PlaneNotFinished) { YourMoney=YourMoney-1000 }

While(PlaneFinished) {
If(PlaneBroken) { YourMoney=YourMoney-1000}
Else {YourMoney=YourMoney-100}
}

You may need to increase the number of zeros depending on model.

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##### Well-Known Member
I wrote a program for calculating costs. Here's the source code for the main loop:

While(PlaneNotFinished) { YourMoney=YourMoney-1000 }

While(PlaneFinished) {
If(PlaneBroken) { YourMoney=YourMoney-1000}
Else {YourMoney=YourMoney-100}
}

You may need to increase the number of zeros depending on model.
I think I found it in graphical form:

#### proppastie

##### Well-Known Member
Log Member
What would others be?

BJC
MY/I=stress at extreme fiber
M=moment
Y=distance centroid to extreme fiber
I=moment of inertia

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#### Christian Moreton

##### Active Member
Christian Moreton,

If you do not like the advice given on here, you do not have to take it. In particular, simply dumping a little math without underlying theory may take one down an undesired path. The background information is usually important.

No one here is required to help you at all. Those that do are volunteering their time and hard earned knowledge to provide you with the references they think you need given your questions. Reply with sarcasm and anger, and you may find their help to you will cease.

In addition, use of the advanced search function may show you that almost all topics have been talked about before, with references, basic knowledge, experience, etc all contributed and discussed. Using searches may find you threads and posts on your exact topic that you may then read, take lessons from, and then contribute to.

Billski
Ya I get it, google is my friend. ok bye. Thanks for no information.

HBA Supporter
Log Member

#### Hot Wings

##### Grumpy Cynic
HBA Supporter
Log Member
"Thanks for no information. "

Wsimpso1 actually provide some very useful information but one has to be able to figure out how to use something a little more advanced than a basic Google search to take advantage of that information.

Other thoughts redacted.........

#### 12notes

##### Well-Known Member
Log Member
Ya I get it, google is my friend. ok bye. Thanks for no information.
I will give you a simplified equation.
$Speed*Weight = (x* (ScaledSpeed)^y *(ScaledSpeed)^z )$

Now, that should work for specific case appropriate values of x, y, and z.

However, finding those values is not simple, and, while you may want an easy to calculate equation with simple straightforward variables and constants, that does not mean that one exists.

When you ask a question and reject quite helpful answers from people whose knowledge of the subject is vastly larger than your own because the answers are too complex or time consuming for you, perhaps you should consider that the question does not have a simple shortcut to get the correct answer, rather than acting as if those who are trying to help you are withholding the secret simple answer for unknown nefarious reasons.

I would like a simple equation to explain what results from combining carbon, oxygen, nitrogen and hydrogen. It sounds simple, but getting a Phd in organic chemistry, reading thousands of books, and a lifetime of research would only get me a partial answer. The simple equation doesn't exist.

Read pages 3-6 of this link on dynamic scaling, already posted by Aerowerx. You can skip all the math, but it should give you an idea of what goes into getting the answer you want.

If you still think that there is a simpler answer, it's sitting at the top of this post. Good luck figuring out x, y, and z for your particular project for a particular flight condition. The equations in the linked paper are easier, and would probably be needed to find those values.

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