In this page you will find more detailed info about the design of a wing and the consequences of changing the shape of the wing.

But first we like to ask your help.

What do we seek?

My wife is guarding some kids during the day. One of the fathers is a JAVA-wiz. He suggested that he could make a JAVA-script if I would give him formulas to use and explain how to use them to get a good estimate of the performance of a airplane design.

I was thinking about a program where you can insert data of the wing and which gives you a view of the wing from above. You will still be able to move the points of the wing and the wingarea and so will automaticly be recalculated. Airfoil data will be inserted by inserting several points of the polar of the airfoil. These data you can find in several on-line calculators. I also want to use data from engines, but I need a list of what kind of thrust of engine-prop combunation will generate. I am thinking about all kinds of sizes; So if you have data of engine-prop-combinations of scale or full-size airplanes, please send them to me.

 


Goal of your design


The Forces

I know that a on-line program to estimate the performance of a design can be usefull to learn more about airplane-design and it could help several beginners with their first steps into aviation and its design. I still have some questions about the theory. If you can help me, pleeeaase, take contact with me and help us to get started. I will mostly use two books as guidance. One is a translation of a paper of Stelio Frati about gliderdesign. The other is a work of a Dutch engineer who give classes in a airplane-design-school. It covers a lot about motorized airplane design. I have a lot of formulas to use. I understand a lot already, but I miss some knowledge. Pleeaase, help us. The time is limited. The kid of the father will be going to school in 2003. I guess that I might loose contact with the (JAVA-wiz) father.

More theory

Changing the size

Everybody dreams of having a replica of some famous airplane. Mustang, Corsair, Fw-190, Mosquito would be just a few on the most wanted list. But I need to warn those who want to make a scaled version. Imagine you would like to make a 1/2 scale version of a Corsair. The wing area and the weight will be less than the original, of course. But the wing area will be 1/4 of the original (1/2 . 1/2= 1/4), while the weight will be 1/8 of the original (1/2 . 1/2 . 1/2= 1/8).

Here you can see that wing area uses two dimensions and weight uses three dimensions. That's why the relation wingarea /weight changes when scaling an airplane.

What are the consequences of these changes in the relation wing area / weight? Well, we need to look at two different situations. First we look at scales larger than 1 (bigger than original). Here the weight rises quicker than the wingarea. This situation leads to larger wing loadings and all its problems (underpowered, high stall speeds, clumsy steering). Secondly we look at scales smaller than 1 (smaller than original). Now we need to look at two different phenomenons. The first is related to what we told you here above. The weight drops quicker than the wing area. This leads to low wing loadings. These planes are livelier than the original. This sounds like fun. But remember that some WW II-airplanes were so lively and agile that they became deadly. Imagine a scale down version of such an airplane in the hands of a beginning pilot. Aaaaaah! Secondly you need to know that scaling an airplane doesn't scale the surrounding air. When using slow wings you need to keep this phenomenon in mind. What happens? An airfoil, which performs very well in a WW II-airplane, can perform less if you scale the airfoil to a hand throw model. What happens around the airfoil? The air around the airfoil separates quicker. You can avoid this situation by choosing an airfoil that is less thick. The Reynolds-number range of an airfoil can help you in your choice of airfoil.

Re =

rho.jpg (829 bytes) . v . k

(formula 40)

n.jpg (781 bytes)

 
  Re = Reynoldsnumber
rho.jpg (829 bytes) = density medium
v = velocity
k = chord
n.jpg (781 bytes) = viscosity medium

This can be simplified to:

Re = k . v . 9360

(formula 41)
  k in feet
  v in mph

Re = k . v . 68695

(formula 42) (corrected in edition 6)
k in metres
v in m/s

Using the smallest chord and the slowest speed you will get the lowest Reynolds number the airfoil has to have. There are many lists on the net where you can find airfoils and their Reynolds number range. Be sure not to forget to check the airfoil when starting a new design. If you use an improper airfoil, you may get stalls earlier than expected and this mistake can be deadly to your model (and/or the pilot).

Also keep in mind that the performance of an airfoil depends of the used Reynolds number. A certain airfoil has a higher maximum Cl when used with larger chords. Remember: larger chords lead to larger Reynolds numbers. When using a smaller airfoil (like RC (=Radio Controlled) -models) the Reynolds- numbers is much lower than when using the airfoil for a full-scale, piloted airplane. So don't use data (like maximum Cl, minimum drag) of an airfoil when they are generated at lower or higher Reynolds numbers. A deadly mistake!

Changing (or choosing) the airfoil

This choice can be difficult, because the choice is enormous. You need to keep several things in mind while choosing an airfoil. First, the Reynolds number. Make sure your situation is located in the Reynolds number range of the airfoil. Secondly, the lift/drag relation. Every airfoil has his typical curve. We will help you in understanding these curves.

The polar

A example of a polar

Several, easy to be found points on the curve can be of great importance to you. Point 1 (Cl max) is easy to find. That's the point on the top of the curve. At this point you can calculate the stall speed. Put Cl max into a variant of formula 1 in formula 2 (see The forces) and you get:

v stall =

haak_l.jpg (891 bytes) W haak_r.jpg (896 bytes) 1/2 (formula 43)
0,5 . . Cl max . S

Point 2 shows the stall of the airfoil. Do not make the mistake by using this point to calculate the stall speed. You really need to use Cl max for that issue. Point 3 is the point with the lowest Cd value. That's the point on the left on the curve. At this point you get the highest speed. Point 4 is the point where the curve crosses the X-axis. Here is the point for a dive. Every point below the X-axis is related to inverted flight.
There are some other interesting points. But these need to be calculated or constructed. Point 5 needs to be constructed. To understand the importance of this point you need to know that in every point of the curve you can determine the glide angle. How? Well, just construct a line from the 0,0 point (crossing of X and Y-axis) to the point. The angle between this line and the Y-axis is the gliding angle. Point 5 is the place where the angle is the smallest. Also is the relation Cl/Cd maximal in this point. Cl/Cd is the glide ratio of the wing. The lower the glide ratio, the lower the needed power to get horizontal, powered flight. So here you can also find the point of best cruising. Remember what I said in the first part of the theory! Don't forget the drag coefficient of the fuselage and all the rest when calculating the exact theoretical glide ratio. You need to use point 5 and increase that Cd with the other Cd's (donít forget induced drag, later more on this item). You could use the obtained glide angle to calculate the length of the landing gear.
Point 6 needs to be calculated. This point is known as the climb ratio. Point 6 is the point where Cl3/Cd2 reaches its maximum. How can you find this point quickly? Just make a spreadsheet (Excel or any similar program), fill in some points of the polar (the more, the better) and let it generate a curve (Cl3/Cd2 on X-axis and Cl on Y-axis). The point on the most right is the maximum we seek.

Theoretical glide ratio

You could already read that finding the glide ratio could be easy to find. It is simply the smallest angle possible between the Y-axis and the line constructed between the origin (point 0,0) and a point on the polar curve. But a simple polar does not contain all the factors of an airplane. You still have to keep in mind the parasite drag of other components (fuselage, wheels, tail) and the induced drag.

Cdi =

Cl2

(formula 44)

pi.jpg (794 bytes) . ar.jpg (732 bytes)

 

You can now calculate the Cd increase, due to the induced drag, for every point of the polar. If you already created that spreadsheet I mentioned, it will not be hard to include this formula into the spreadsheet.

For the additional parasite drag, due to the other airplane components, you need to correct the Cd values you can find in the list placed in "The forces". These values are related to the frontal area, the formula for drag (formula 12) is related to the wing area.

Cdc =

Cd . A

(formula 45)

S

 
  A = frontal area
Cdc = corrected drag coefficient

You can use this correction on any airplane part.

CD (the total airplane drag coefficient) is the result of the Cd of the wing (polar), Cdi (induced drag) and the sum of all the corrected drag coefficient
(formula 46)

When you construct the curve off the total airplane drag, you can search for the theoretical glide ratio by constructing a line from the origin (point 0,0) that touches the curve. The glide angle is at this point is the smallest. The Cl/CD ratio at this point is the theoretical glide ratio of the complete airplane.

Another angle, the effective angle of attack of the complete airplane can also be calculated. But do not mistake this angle with the geometric angle of attack (= true angle between horizontal and airfoil).

alpha.jpg (779 bytes)eff = alpha.jpg (779 bytes)geom - alpha.jpg (779 bytes)i

(formula 46)

Look out about the interpretation of this formula. I don't say that the angle of attack gets less when the induced drag is larger. I say that the angle used effectively by the wing (used to create lift) gets less when induced drag gets larger. So you need more geometric angle to create the same lift.

alpha.jpg (779 bytes)i =

Cl

(formula 47)

pi.jpg (794 bytes) . ar.jpg (732 bytes)

 

Choosing your wing area

Still working on this one.

Changing the wing form

As you could see in the first part, there are a few factors that you can change once you decided what wing area you want to use. Aspect ratio and taper (multi or single taper). The choice of aspect ratio has many consequences. OK, you can choose ultrahigh or ultra low or a "normal" medium. Each has his pro and cons.
Ultrahigh will lead to very short chords. This long, slim wing leads to heavy spars. Also remember what I said about Reynolds. The smaller the airfoil, the more problems about air separation at low speeds. But the higher the aspect ratio the smaller the induced drag and that is a good point. The smaller the induced drag the smaller the induced angle of attack (see above). So the shorter the needed landing gear.
The lower an aspect ratio the compacter the airplane and the larger the airfoil. Using this large wing you could use a lighter spar (higher spar are stronger and can be made lighter to have the same strength). Cockpit could be integrated into the wing, which will produce less parasite drag. But low aspect ratio has a high-induced drag. High-induced drag means higher induced angle of attack. This means a longer landing gear. Low aspect ratios can fly under a greater angle than the high aspect ratios, so they can use their wing as an airbrake. Due to this there is no need for high-lift devices on a low aspect ratio, so the construction is made easier. They can fly slower, but there is many power needed to keep them in the air under this condition.

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