Yet More Math Help

[CloudyIFR]

Good Morning,

If I have the below formula:

7 = (5*2+7)-XX*2 / 12

How do I rearrange the formula to find XX?

Happy Holidays
Curtis

[biber]

XX = 60

?

biber

[CloudyIFR]

Would you mind rewriting the formula with XX on the left of the equals for me?

Thanks
Curtis

[biber]

I did go the following way:

7 = (5*2+7)-XX*2/12 ; 5*2 equals 10 and 2/12 breaks down to 1/6

7 = (10+7)-XX/6 ; 10+7 equals 17

7 = 17-XX/6 ; adding XX/6, subtracting 7

XX/6 = 10 ; multiply by 6

XX = 60

Or you write it out that way (just rearanged, nothing solved or evaluated):

-(7-(5*2+7))*12/2 = XX


biber

[CloudyIFR]

I think I made a mistake that may make a difference, it should be:

7 = ((5*2+7)-XX*2) / 12

note the parenthesis.

Thanks
Curtis

[biber]

Hm,

XX = -67/2

?

7 = ((5*2+7)-XX*2) / 12 ; multiply by 12

7*12 = (5*2+7)-2*XX ; subtract (5*2+7)

7*12-(5*2+7) = -2*XX ; Divide by -2

-(7*12-(5*2+7))/2 = XX

biber

[CloudyIFR]

Perfection! Thank you!!!

[CloudyIFR]

Alright, I have another math problem

If I have a wing that is single taper I can calculate the sweep angle however, what if I have a wing with multiple panels i.e. different chord lengths and spans.

How do I figure the sweep angle of a multi panel wing? Can I calculate the angle of each panel and then divide by the number of panels? or is it a weighted average?

Thanks
Curtis

[JetPlaneFlyer]

Alright, I have another math problem

If I have a wing that is single taper I can calculate the sweep angle however, what if I have a wing with multiple panels i.e. different chord lengths and spans.

How do I figure the sweep angle of a multi panel wing? Can I calculate the angle of each panel and then divide by the number of panels? or is it a weighted average?

Thanks
Curtis
Assuming your objective is to calculate dihedral effect:-

Take the moment of area of each panel (that's the panel area multiplied by the distance between the fuselage centre line and the centroid of the panel area ) and multiply this by the sweep angle of the panel in question.
Do the same for all the panels in the wing semi-span and add the results together.

Divide the resultant figure by the total moment of area for the wing semi-span (that’s the same as the above calc but without the wing sweep multipliers)

e.g.

(Ma1 . S1) + (Ma2 . S2) / Ma1 + Ma2

Where:
Ma1 = Moment of Area panal 1
S1 = Sweep angle panel 1
Ma2 = Moment of Area panal 2
S2 = Sweep angle panel 2

The resultant should be the aerodynamic effective average sweep angle (or whatever it’s called).

I’ve never tried this as my swept wings have all been one panel jobs, but I think the principal is sound.

[Texas Buzzard]

Alright, I have another math problem

If I have a wing that is single taper I can calculate the sweep angle however, what if I have a wing with multiple panels i.e. different chord lengths and spans.

How do I figure the sweep angle of a multi panel wing? Can I calculate the angle of each panel and then divide by the number of panels? or is it a weighted average?

Thanks
Curtis
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Why would you want to do that? A good estimate is good for modeling purposes - hey it's not a F-22.....just joking. Sweep angle of 3 degrees is equal to 1 degree dihedral OR 30 dgrees sweep = 1- degrees dihedral ( both panals have 10 degrees dihedral - OK?

[CloudyIFR]

Texas Buzzard,

I understand the dihedral estimation is close enough for government work but I needed to know the sweep for a multi panel wing which I didn't know how to figure. But I think I got it and will add it to my Sailplane Calc spreadsheet.

Have ya seen the spreadsheet and review in the April RCSD?

Curtis
Montana

[JetPlaneFlyer]

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Sweep angle of 3 degrees is equal to 1 degree dihedral

Like i said in a previous thread... it's not that simple. The effect of sweep varies with Coefficient of lift. I gave the formula for working it out and some typical figures for different Cl values in the same post so why persevere with the 3 deg = 1 Deg over simplification?

Just in case you missed the post: http://www.rcgroups.com/forums/showthread.php?t=833590&page=2 #17

[BMatthews]

Curtis, keep in mind that small amounts of sweep angle do not have anywhere near the same degree of stabilizing effect as small amounts of dihedral. The whole equivalence thing is clouded in much mystery. I've seen various equivalence angles and flown some models with crescent shaped wings and the equivalent dihedral on those wings is lost in all the other flight issues if there is any.

For example, go ask the Zagi flyers if they notice any large degree of self leveling in thier wings if left in a bank. I'd say you'll find that there's no real noticable effect.

Couple that with the idea that it's also related to the lift coefficient and it's one of those things that isn't worth worrying about unless you're doing a scale jet fighter like an F86 or other design with huge amounts of sweep.

But to answer your question it stands to reason that it would be a weighted effect. On a typical 5 panel wing the center section would have no sweep, the mid panels would have 2 or 3 degrees and the sharply raked tips would have more like 25 to 30. However again the tip panels are so short that I doubt the air will see the sweep to the same degree as if they were longer with the same sweep. But that's more my gut reaction rather than something I've seen analyzed.

[Brandano]

Also, differently from the dihedral effect, the sweep effect is reversed at a negative AOA

[JetPlaneFlyer]

Curtis,
It just occurred to me that the calculation i proposed earlier considers only panel area and moment arm. I neglected to factor in the Cl distribution along the span of the wing. The calc should work ok if your planform has roughly elliptical chord distribution as then all the wing will be operating at similar Cl but for wings that differ significantly from elliptical then Cl will differ along the span so the calc would not be accurate.

The sweep angle itself also effects Cl distribution along the wing but factoring this in is beyond me .

I wish my math was better:o

Steve

[CloudyIFR]

I appreciate all the math help and have another one.

Taper Ratio is tip chord divided by root chord.

If there is a multi tapered wing how do you calculate the TR?

Let's say we have a two panel wing with the following dimensions:
This is for one half of the wing. Total one-half span is 30'.

Panel 1 (inner panel)
Root Chord 10"
Tip Chord 8"
Span 20"

Panel 2 (outer panel)
Root Chord 8"
Tip Chord 8"
Span 10"

Do you just take the TR for each panel then divide by 2 or take a weighted average of it.

Thanks
Curtis

[biber]

In my book it is still what you said:

Taper Ratio is tip chord divided by root chord.

Simple as that.

biber

[HugePanic]

i can give you an formula to calculate the MAC and Xn25 if it help....
(maybe you can do your calculations with that information)

[CloudyIFR]

i can give you an formula to calculate the MAC and Xn25 if it help....
(maybe you can do your calculations with that information)

That'd be great.

Thanks
Curtis

[HugePanic]

ok, i post it when i am back at home.

[CloudyIFR]

In my book it is still what you said:

Simple as that.

biber


Just to make sure we're on the same page here.

Attached are three screenshots.

The first two are wing examples.
So the Taper Ratio is still the most outer tip chord divided by the most inner root chord?

The third screenshot is the formula I'm trying to put into a spreadsheet. The spreadsheet is complete and proven accurate for a single panel/tapered wing. I'm trying to get the Taper Ratio worked out for a multi panel/tapered wing.

What significance in error is there? Is it marginal, if so I'll just leave it as is.

I'll run more tests later but seems there should be a formula to calculate the taper ratios of a multi-panel.

Thanks for reviewing this for me!
Curtis "Not a Math Guy"

[biber]

I think the formula simply does not cover the case of multiple taper.

But then again, I don't know much about that particular formula in the first place.
(e.g. the area of application)

biber

[HugePanic]

enjoy......
(learn german the easy way...)

lnü is MAC
xE is the translation of the MAC's leading edge to the original airfoil

the formula is valid for two segmentet wings.

[Brandano]

The most important question is: what do you need the taper ratio for? I suppose you could work out an "equivalent" taper ratio by making a weighted average of the single panels based on their individual area, but is this number actually useful for your scope?

[CloudyIFR]

Brandano,

In post #21 the third photo shows the formula I'm working with.
The Taper Ratio is used along with Aspect Ratio, airfoil pitching moments and zero lift angles to determine desired twist for a flying wing.

Would you mind helping with the "equivalent" taper ratio formula as I do think it would help, at leat I could throw it at the spreadsheet and see the results.

Thanks
Curtis

[Brandano]

Ah, the problem there is that you probably need to take also wing sweep into account, since the more swept the wing is the less twist will be required to make it stable. This becomes quickly very complex.

[nmasters]

Ah, the problem there is that you probably need to take also wing sweep into account, since the more swept the wing is the less twist will be required to make it stable. This becomes quickly very complex.
Curtis' spread sheet uses, and expands on, the formula commonly attributed to Walter Panknin. It takes a lot of features into account, including sweep. It works pretty well for calculating the washout needed for a single panel swept flying wing. As you said it gets complex but at least it's just algebra the Horten method is calculus.

--Norm

[CloudyIFR]

Ah, the problem there is that you probably need to take also wing sweep into account, since the more swept the wing is the less twist will be required to make it stable. This becomes quickly very complex.

Yep, like Norm says the Panknin formula in Post #21 does take that into effect as well as my spreadsheet.

If you wish to view the spreadsheet for a single panel wing visit here and download "Flying Wing Calc".

http://h1.ripway.com/cloudyifr/files.htm

Brandon I think that formula would be very helpful.

Thanks
Curtis
Montana

[Brandano]

And how do you deal with panels set a different sweep, in order to get an average sweep? Anyway, the simplest way to get a weighted average by wing surface would be to multiply each value for its relative surface area, and then divide the sum of these values by the total wing area.

[CloudyIFR]

And how do you deal with panels set a different sweep, in order to get an average sweep? Anyway, the simplest way to get a weighted average by wing surface would be to multiply each value for its relative surface area, and then divide the sum of these values by the total wing area.

I believe it's the same as you just explained. Heck, I could have figured that out for myself!!!

We're still pondering and testing whether that's accurate enough for Dr. Panknin's formulas. But that's the only way I know of how to figure a multi-panel wing with his proven formula for a single tapered wing.

Curtis
Montana

[CloudyIFR]

Is this accurate?

2*(Avg Chord/Root Chord)-1

Curtis

[nmasters]

Yes but... I'll have to get back to you, I'm supposed to be doing something “productive” right now :(

--Norm

[nmasters]

And how do you deal with panels set a different sweep, in order to get an average sweep?
To find the average sweep of a two panel wing graphically you find the aerodynamic center of each panel and then draw a line from the AC of the inboard panel to the AC of the outboard panel. The sweep of the line is the average sweep. It's the same graph used to find the AC of a multi panel wing. When you see it all on one page it looks terrible but the steps are simple.

--Norm

ps I'm still working on the response to post #31. I'm downloading NACA TR 572 (http://ntrs.nasa.gov/search.jsp?R=958663&id=9&qs=Ne%3D25%26N%3D197%2B286) right now

[nmasters]

Yes but...
The multi taper is going to affect the spanwise position of MAC and thus the wing pitching moment. The last sentence on that scan points out that the bending moment (equivalent to the swept 'wing pitching moment) won't change much for similar planforms but to be accurate in its CG recommendation I think your spreadsheet needs to consider each panel individually and then find the average AC. The proses (graphical and mathematical) is shown in appendix A of “Model Aircraft Aerodynamics” pgs 249 and 250 of the third edition.

See I do site my sources... when I can find them :rolleyes: :o

--Norm

[CloudyIFR]

Edit
The proses (graphical and mathematical) is shown in appendix A of “Model Aircraft Aerodynamics” pgs 249 and 250 of the third edition.

--Norm
Well I have the second edition and mine i Appendix 1 but that's exactly how it is figured. So far so good! :-)

Curtis

[CloudyIFR]

Alright, here we go again.

I need some math help.

I've worked this as much as my headache will allow. :-)

Anway, I just can't seem to figure it out, even with reading all the posts from the excellent help I've received before.

15.98 = ((0.54 *0.1+0.46*0.1)-0.6 * 0.05)/0.004381

What I'd like to do is have the formula find the 0.1 value. I know all the other values.

So how do I swap the 0.1 and 15.98 values?

I'm using an excel spreadsheet if that helps.

Thanks
Curtis

[Montag DP]

Alright, here we go again.

I need some math help.

I've worked this as much as my headache will allow. :-)

Anway, I just can't seem to figure it out, even with reading all the posts from the excellent help I've received before.

15.98 = ((0.54 *0.1+0.46*0.1)-0.6 * 0.05)/0.004381

What I'd like to do is have the formula find the 0.1 value. I know all the other values.

So how do I swap the 0.1 and 15.98 values?

I'm using an excel spreadsheet if that helps.

Thanks
Curtis0.1 = (15.98*0.004381 + 0.6*0.05)/(0.54 + 0.46)

Steps:

1: Multiply both sides by 0.004381
---> 15.98*0.004381 = 0.54*0.1 + 0.46*0.1 - 0.6*0.05

2: Add 0.6*0.05 to both sides
---> 15.98*0.004381 + 0.6*0.05 = 0.54*0.1 + 0.46*0.1

3: Factor out 0.1 from the right side
---> 15.98*0.004381 + 0.6*0.05 = 0.1*(0.54 + 0.46)

4: Divide both sides by (0.54 + 0.46)
---> (15.98*0.004381 + 0.6*0.05)/(0.54 + 0.46) = 0.1

[CloudyIFR]

Montag DP,

Thanks so much! It fits perfectly.

I'm working on making a Flying Wing Plank Calc spreadsheet.

This way the modeler can input their planform, weight, desired speed, Lift Coefficient and Static Margin and the spreadsheet will tell the modeler what airfoil to choose!

Curtis
Montana