How to Calculate Airfoil Ordinates

8/8/2019 How to Calculate Airfoil Ordinates

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How to Calculate Airfoil Ordinates

Part 1 of this series provides some background and provides sources for obtaining airfoil

ordinates.

Some airfoils have a large number of ordinates. I've seen sets of ordinates having over 1,000 points. If you are manually plotting an airfoil you do not have to plot every ordinate. You

only need enough so that you can draw the airfoil with reasonable accuracy.

I would say plotting 20 points each top and bottom is accurate enough for most airfoils. In

areas where there are tighter curves you should plot points closer together. Examples arenear the leading edge or the reflexed portion of that type airfoil.

Coordinate Standards

Airfoil ordinates are simply points that define the shape of the airfoil. The numbers are given

in percentage of the wing chord. There is more than one standard, but they are all easy to

figure out.

The standards I know of are as follows:

1. Stations from 0% to 100% chord. In this case, multiply the chord of the airfoil you

are plotting times percent of the station/ordinate pairs in percent. In other words, if the number given is 1.25 then multiply times 1.25%. If your calculator does not have

a percent key, then multiply times 1.25 and then divide by 100.

Ordinates of this type are presented in two sets of ordinate pairs - one for the upper portion of

the airfoil and one for the lower.

2. Stations from 0 to 1. In this case it is straight multiplication of the chord times each

of the station/ordinate pairs. This standard also differentiates between the top and the

bottom of the airfoil.3. The last example is the style used for computer programs. This is listing of ordinate

pairs with no differentiation between the top and bottom of the airfoil. Numbers arefrom 0 to 1. The listing starts at the trailing edge of the airfoil and moves forward

defining the underside of the airfoil and then the leading edge, the top of the wing and back to the trailing edge again.

It sounds more complicated than it is - again, it is simple multiplication.

Calculating the Ordinates to be Plotted



For this example I will be plotting a NACA 2412 airfoil. The NACA 2412 is a semi-symmetrical airfoil (cambered) that is stable and somewhat fast although it would not be the

best choice for an extreme speed aircraft. It would be a good choice for a one-design clubracer because it has no bad habits and will not get to speeds that the average pilot can't

handle.

The first table below is the set of ordinates for the NACA 2412. The listing uses standard (1)above.

I will be calculating ordinates for and plotting an airfoil having a 9" chord. Multiply all

stations and ordinates by the chord. Again, the numbers given in the ordinate listing are

percentages. That means you multiply the chord by the station or ordinate in percent.

To find the second station for example, multiply 9" x 1.25%.

The leading edge (L.E.) radius is also multiplied by the chord to get the actual radius. This isalso a percentage.

The second table contains the resulting numbers after multiplying them by the wing chord.

All numbers are in inches for this example. Calculating and plotting works the same

regardless of your number system.

NACA 2412 Ordinates

Upper surface Lower surface

Station Ordinate Station Ordinate

0 0 0 0

1.25 2.15 1.25 1.65

2.5 2.99 2.5 - 2.27 5.0 4.13 5.0 - 3.01

7.5 4.96 7.5 - 3.46

10 5.63 10 - 3.75

15 6.61 15 - 4.10

20 7.26 20 - 4.23

25 7.67 25 - 4.22

30 7.88 30 - 4.12

40 7.80 40 - 3.80

50 7.24 50 - 3.34

60 6.36 60 - 2.76

70 5.18 70 - 2.14

80 3.75 80 - 1.50

90 2.08 90 - 0.82

95 1.14 95 - 0.48

100 0 100 0

L.E. radius: 1.58

Slope of radius through L.E.: 0.10

NACA 2412 (9" Chord)

Upper surface Lower surface

Station Ordinate Station Ordinate

0.000 0.000 0.000 0.000

0.113 0.194 0.113 -0.149

0.225 0.269 0.225 -0.204 0.450 0.372 0.450 -0.271

0.675 0.446 0.675 -0.311

0.900 0.507 0.900 -0.338

1.350 0.595 1.350 -0.369

1.800 0.653 1.800 -0.381

2.250 0.690 2.250 -0.380

2.700 0.709 2.700 -0.371

3.600 0.702 3.600 -0.342

4.500 0.652 4.500 -0.301

5.400 0.570 5.400 -0.248

6.300 0.466 6.300 -0.193

7.200 0.338 7.200 -0.135

8.100 0.187 8.100 -0.074

8.550 0.103 8.550 -0.043

9.000 0.000 9.000 0.000

L.E. Radius = 0.142



This particular airfoil has stations that are identical for both the upper and lower surfaces butthat is not always true. Be sure to pay attention to what you are doing. I have made the

mistake of assuming the stations were the same when they weren't which resulted in somestrange airfoil plots.

Now that you have the numbers they need to be plotted on paper. The ordinate/station pairs

are simply (x, y) coordinates. The Station is X and the Ordinate is Y.

How to Make a Set of Ribs for a Tapered

Wing

There are several ways to fabricate a rib sets for tapered wings. The method shown here is

the fastest and one of the most accurate. The only drawback is that the ribs must be evenly

spaced assuming all the ribs are the same thickness.

If ribs are needed that do not space equally then you will have to interpolate those ribs from

the surrounding ribs or glue an over-sized blank in place and then sand it to shape with the

wing panel.

Another way to make ribs for a tapered wing is manually plot or use rib-plotting software todraw each rib pattern individually. The ribs are then cut in pairs. This is my least favorite

way as it is the most time-consuming, tedious and presents more opportunities to makemistakes.

The method being presented requires two airfoil patterns for an entire wing panel instead of one for each rib. The idea is to shape all the ribs between the two patterns.

The number of blanks can be determined one of two ways:

Method 1: Determine the wing span. Determine the rib spacing. Divide the span by the rib

spacing and add two.

For example, if you are building a 56" wing having ribs spaced 2" apart then you would need30 ribs (15 per panel).

y Number of ribs = (wing span ÷ rib spacing) +2

Method 2: Cut a random number of blanks and then space them equally to make a wing of

the desired span.

Also see

y How to Make a Set of Ribs for a Constant Chord Wing

y Styles of Model Aircraft Wing Construction



y About Airfoils used with Flying Model Aircraft

Preparing the templates

Make copies of your drawings and spray

glue them to a hard template material.Aircraft plywood, Formica or aluminum

are good choices.

In this case, I used 1/8" aircraft

plywood.

Take your time shaping the

templates to make them as accurate

as possible.

Depending on how you do things, it mayor may not be important that the

centerlines of the ribs are aligned to one

another as they will be in the finished

wing.

For example, if you cut spar

notches after the ribs are sanded toshape and separated from the

blanks then the templates do nothave to be perfectly aligned now.

I will be cutting the spar notcheswhile the ribs are clamped between

the blanks and am incorporating a

slight degree of washout in the

wing, so I aligned the tip rib over

the root rib accordingly.

This wing will also be swept, but

the templates do not need to be

aligned to reflect that. I aligned the

ribs so that the 33% lines are

aligned.

With the templates screwed or double-

taped together, drill holes for clamping

bolts.

Always save your templates.



Making the Ribs

If you want to save wood you can estimate

the size of each blank. I find that to be too

much trouble and simply cut each blank to

the maximum size.

The blanks were drilled in batches

using the template as a guide.

Remove four blanks from the stack.

Cut around the templates to make two root

and two tip ribs. These will be the actual

root and tip ribs.

I usually make them from a harder balsa and they become built-in sanding

templates when sanding the wing using a

long block.

Put these ribs aside. They do notget clamped between the templates

with the rest of the blanks.

Separate the remaining blanks into two

stacks. Bolt one stack together between

the plywood templates.

There are twelve 1/16" blanks in

this stack.

When you make the matching set,turn the templates to be mirror

images and bolt them together sothey taper the opposite way.

This helps ensure that any material

removed from the templates when

sanding the first set doesn't affectthe second set.

Begin by planing and carving to rough

shape. All I've done to this point is use a

razor plane.



Use a good sanding block to finish the set.

Avoid sanding the templates.

I blocked up the trailing edge to

level the centerline and then ran the

set through my table saw to cut the

spar notches.

In the past I used a razor saw to cut

the sides of the notches and a hobbychisel to chip out the waste.

The ribs have a taper around the edge that

must be removed.

There are two ways that I might do

it.

y Pull matching ribs from

both sets and sand them

together.

y Sand the taper off after the

wing panel is built which is

probably more accurate.

Any spars on the building

board will have to be

blocked up to clear the

tapered area. Otherwise thespar will stand proud when

the taper is sanded off and

will have to sanded down.Sanding down spars is nofun. Make them flush or

even too low but never toohigh.

How to Edge-Join Balsa Sheeting to make a

Skin

Joining balsa wood sheets to make a skin is all but unavoidable for many flying model

aircraft. This is one of those tasks that seems deceptively simple² just edge glue some

sheets that are the same thickness, grain and roughly the same hardness or weight and you

have a skin.



While that's basically all there is to it, accomplishing the task successfully is unfortunately

more difficult than it sounds and is rife with hazards and pitfalls² all of which are very

visible in the final product.

Skin Defects

y Unsightly gaps between the sheets.

y Visible ridges at the seams.

y Skin is sanded too thin in some areas which significantly weakens the skin and creates

undulations.

All the above problems are nearly impossible to fix without replacing the skin. Laminating

new wood over a thin spot will usually make the problem worse, for example.

It is always better to discard a poorly made skin rather than forcing the issue. Once the skin

is glued to the structure it is hours of work to cut it away and sand off glue to get back down

to the structure. This is one of those areas where discipline and patience will pay off.

Always make the skin as a separate component if possible. Some instructions indicate the

balsa is joined as it is glued in place. That is the worst possible way to join a skin and makes

it very difficult to sand a smooth seam.

Better is to complete the skin including sanding prior to gluing it in place. You should only

have to do some touch-up and finish-sanding near the end of construction.

Preparation

What I've learned is that success in making a balsa skin, like so many other model buildingtasks, is a matter of preparation more than anything else.

The first thing you should do is gather wood having the appropriate weight, grain and

thickness for the skin. Sheet wood can add a lot of weight to your model in a hurry.

Generally speaking the sheets you choose should be the lightest, straight-grained (A-grain)

balsa in your stock. A skin adds a lot of strength to the model as well. Contest balsa is

perfectly acceptable in most cases.

Matching Sheet Thickness

The biggest problem I had was that the actual thickness of balsa sheets varies enough that the

edges sometimes have an extremely poor match. Until I started paying more attention to thisI had to do too much sanding which caused low spots and other imperfections. The less you

have to sand the skin to level the joints and smooth it the better it will be.

If you actually check your balsa stock you will find that that many balsa sheets taper slightlyacross the sheet. This is something that happens at the mill. That doesn't mean the wood

should be discarded. You can use it for components other than skins.



To determine if a sheet is acceptable check both of its edges against both edges of another sheet. If any edge doesn't match then one or both of the sheets should not be used. Select a

third sheet and check both sheets against it in the same manner. Continue doing this until youhave enough sheets to make the skin that match reasonably well.

By the time you have selected your sheets, the thickness of both edges of any given sheet

should match the thickness of both edges of every other sheet for the same skin. When youhave enough sheets to make the skin that match within reason put them aside and repeat the

above steps to select sheets for the rest of the skins. A typical wing may need 4 skins, for

example.

Ideally all edges of all sheets should match all skins used for matching components. In other

words, if you're making wing skins then all the sheets for the upper skin should also match all

the sheets for the lower skin, but that may be asking too much.

The next thing you should do is weigh each stack of sheets so they can be matched to help balance the wing. If you selected the wood properly the skins should be fairly closely

matched in weight.

It's up to you how anal-retentive you want to be about all of this. I match each skin and then

weigh the stacks. If they're close then I move on. If not then I mix and match sheets until the

stacks are close to the same weight. Now I check thicknesses again. If they match then I

move on. if they don't match then I work on something else for a while and come back to it

later.

Joining Balsa to Make a Skin

Now that you've selected the sheets more preparation is necessary prior to joining them.

True the edges of the sheets in

preparation for joining them. If theedge is severely out of true then I

trim it straight using a straightedge and razor blade. Trimming with a

knife doesn't make an edge that'strue enough to join.

I use an edge-truing fixture to sand

the edges perfectly straight andsquare. You can also use a longsanding block , but this takes some

practice to prevent unintentional bevels or rounding over.

If you tightly pull two sheets together that

do not have straight edges then the skin

will buckle ² a condition which is nearly



impossible to sand out.

These two sheets are pressed against each

other to check their fit which is now nearly

perfect.

It's a good idea to mark the edges

that join with numbers or colored

markers so you know which sheets

join to which.

Use short strips of masking tape to hold

the sheets together. They should be snug

but not too tight. If you pull the sheets too

tightly together the skins can buckle. It is

also nearly impossible to press the joints

flush.

Flip the skin over and apply a piece of tape

the full length of the joint.



Remove the tape from the first side so that

glue can be applied in the seam.

Be sure to have a solvent for the gluehandy as well as some paper towels. A

fast evaporating solvent is best.

I use traditional model airplane glue such

as Ambroid or Sigment for joining balsa

skins. Nothing works better. It dries fast,

is plenty strong and sands easily without

leaving unsightly ridges that harder glues

will cause.

Open the joint so glue can be applied. I

like to use a few weights to hold the skin

in place so I can use both hands to guide

the glue.



Apply a liberal bead of glue in the joint.

Close the joint immediately and press the

skin flat on the workbench.

Put some solvent on a paper towel to clean

up all the glue that oozed out of the joint.

This will save you all kinds of problems.

For example, if you do not do this and

simply start sanding the joint, glue blobs

can break loose and leave deep gouges in

the skin.

While you're wiping up the glue besure to press the joints as flush as

you can get them.



Allow the solvent a short time to

evaporate. Apply strips of masking tape

across the joint. I flip the skin over to

remove the tape running along the joint

and replace it with tape going across the

joint for two reasons:

y The glue will dry faster. y The solvent in the glue will melt

the glue on the tape leaving

melted tape goo on the wood.

When the glue has dried thoroughly

remove the tape carefully to avoid

gouging the wood. If there is tape

goo or excess glue outside the joint

then quickly wipe the joint withmore solvent. Don't overdo it or

you'll melt the glue in the joint

which may cause the sheets toseparate.

Although it's not shown here you shouldalways sand both sides of the skin before

gluing the skin to the model. Be sure to

level all the joints and get the skin as

smooth as possible.

If you can't level the joints when

the skin is flat on your workbench

then you'll never get them level

after the skin is glued to the model.

Use a large sanding block starting with

relatively coarse sandpaper. I normally

begin with 120 or 150 grit and work my

way to 220 grit sandpaper prior to gluingthe skin on. Always sand with the grain.

Leave finish sanding until the skin

is in place and the model is nearlycomplete.

A nice gapless skin. This is the upper

hatch of an SR Batteries Fokker Eindecker .

Unfortunately, the laser-cut skins don'tmatch in color, but it shouldn't be a

problem in this case because the deck will

be covered with aluminum.

By the way, I've never seen laser

cut wood with edges that match as

closely as I'd like them too.

Additionally, if you don't sand the

burned edge away then the seam



will be very dark and will probablyshow through most film coverings.

How to Calculate Airfoil Ordinates

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