Help with Wing area vs. Tail surface areas ? Please?

[IMoonBark]

Please bear with me as I attempt to understand…. I am seeking the ratio of the tail surfaces in relation to the wing area of my sailplane.

Mar 22, 2004, 04:50 PM #2
Ollie
Registered User
Join Date: Apr 2002
Location: Punta Gorda, FL
Posts: 2,471

“Here are the equations courtesy of Dr. Mark Drela to find out the answers.

"Ch = (A_hori/A_wing) * (tail_arm/avg_wing_chord)
Cv = (A_vert/A_wing) * (tail_arm/avg_wing_span )

"A well-sized tail will be in the range...
Ch = 0.35 - 0.50
Cv = 0.02 - 0.035
If the Ch and/or Cv are below the minimum values, the handling will suffer."

A_hori is the area of the horizontal tail.
A_vert is the area of the vertical tail.
A_wing is the area of the wing.
tail_arm is the tail moment arm. It is the fore and aft distance measured from 25% of the average wing chord to 25% of the average tail chord.”



My wing….

Chord at root = 8” , chord at tip = 4”, constant taper, average chord =6”
Wing span = 96” , wing area = 576 sq. in.

Tail moment arm = 27” from 25% of wing chord to 25% of stabilizer chord.

The average of Ch=0.35 and Ch=0.50 (0.35+0.05) /2 = 0.425=Ch for a middle of the range area of the horizontal stabilizer.

To find the area I plug in the known values:

0.425 = (x / 576) * (27 / 6) or
0.425 = (x / 576) * 4.5 to isolate x divide both sides by 4.5
0.425 / 4.5 = (x / 576) then multiply both sides by 576 ?
(0.425/ 4.5) * 576 = x
(sorry not an arithmetic major)
x = 54.4 sq. in. , wing area to horizontal stabilizer area … Ratio = 10.6 : 1

This seems small to me, I was thinking more along the lines of 7:1 or 8:1

The vertical stab has me even more confused….

Checking the formulas above we find:

Cv = 0.02 - 0.035 Average would be Cv = 0.0275

Cv = (A_vert/A_wing) * (tail_arm/avg_wing_span ) so …..

0.0275 = ( y / 576 ) * (27 / 96)
0.0275 = (y / 576 ) * 0.28125
0.0275 / 0.28125 = (y / 576)
0.0978 = (y / 576 )
0.0978 * 576 = y

y = 56.32 sq. in. This value looks closer to what I would expect for the vertical surface but how could it be greater in area than the horizontal surface??

576 / 56.32 = 10.23 : 1

PLEASE HELP?? Is my math just really Bad? I was thinking horizontal stab area somewhere around 72 sq. in to 82 sq. in. not 54 ????

[IMoonBark]

I just realized that I posted this under the "Airplanes - Electric > Beginner Training Area" and although I am indeed constructing my first electric power sailplane this question would be more appropriate in the "Sailplane" section.

Should I just blank this post out and repost it there? (Or is there a moderator / Administrator that could perhaps move the thread?) I hate making a pest of myself when it is unintentional.

Any help would be appreciated, please don't start throwing rocks just yet.

Imoonbark

[Sunspot]

You think YOU are confused...... :eek:
All this time I have been just charging up and flying my plane. :D
Spot

[Mark Wood]

IMoonBark:
Welcome to RCGroups!

You'll likely get some good answers in Modeling Science where this stuff is discussed in detail so I'll move it there for you. :)

mw

[IMoonBark]

Thank you for the welcome and the "Bump" to "Modeling Science".

WOOT! A thread that I have not yet perused!

I have hopes to learn much, RC Groups is fantastic!!

Imoonbark

[Sail 'n Soar]

Just checked out your Ch math and it is correct. Remember that your AR is 16, so you don't need the big horizontal that you would with a lower, less sailplane-like aircraft. Second, you didn't really describe your flying experience level. You took the simple average of .35 and .5 to come up with the Ch you used in your calculation. Personally, I just use .5 with the CG at ~ 30% for about everything but strictly scale and end up with nice flying aircraft. The .5 will give you a more stable aircraft and lower toward .35 will give you a less statically stable aircraft, unless you push the CG forward. Use .5 and your horizontal area comes up as 64 sq in. No need to go larger.

In terms of the verticle vs. horizontal areas, good point at identifying the inconsistency. Equal areas would be the equivalent of a 90 degree included angle V-tail. When was the last time you saw any design with a smaller included angle? Enough said. If you calculate Ch using the 56.32 sq in vertical stab area equivalent you get Ch = .44, a better number in my opinion.

[Sail 'n Soar]

Just checked out the ratios from published figures for full size sailplanes. The charts show Ch ranges from .3 to .53, with the Janus C at ~ .33 and the Mosquito and PW-5 at ~ .53, for example. The majority of sailplanes graphed appear to lie between .4 and .5, with examples of those between .45 and .5 being the DG 800S, Ventus B, ASH 26, ASW 22, Phobus B, Kestrel 604 and 401. Since these craft have much longer time constants, with the pilot directly on board, any reason you need to make your craft less stable?

For the sailplanes covered in my data CV's are between .03 and .08 except for the DG800S, which exceeds .085. In general there appears to be a bias toward the larger values. Before you start designing with larger verticals, full scale verticals seem to be larger than in model practice, although I have designed models very successful with Cv's ~ .07. VERY responsive to rudder.

[IMoonBark]

Thank you very much, most helpful indeed!

Back to alter the designs to bring them more in line with what has been proven.

Then we get to make more mess! :)