### V-tail sizing example - but is it correct?

Hi guys,

I'm currently designing a kind of motor glider (ish) and am planning on using a v-tail.

I wanted to ask your opinion on the sizing of the tail that I've come up with and I'll run through some figures that I've used.

Here's some useful numbers:

Wing area (Sw) = 6000 cm2
Wing span (b) = 200cm
Distance from tail Aerodynamic Centre to aircraft Centre of
Gravity (L(h/v)) = 62cm
Mean Aerodynamic Chord = 30cm

From Mark Drela's post on the Charles River RC website (http://www.charlesriverrc.org/articles/design/markdrela_vtailsizing.htm) we know that a v-tail area needs to be the sum of the horizontal and vertical stabiliser areas.

So, I need to work out a good area for these.

I've gone with 20% of wing area for the horizontal stabiliser and 10% for the vertical. These numbers were taken from here: http://www.airfieldmodels.com/information_source/math_and_science_of_model_aircraft/rc_aircraft_design/step_by_step_model_aircraft_design.htm

This gives me the horiztonal stabiliser area (Sh) as 1200cm2 and the vertical stabiliser area (Sv) as 600cm2.

Summing these gives 1800cm2 and as I'd like a base of 20cm of the tail on the fuselage that gives me 45cm length on each side. If you also follow the angle calculation on Mark Drela's post then you get 35 degrees from the horizontal or 110 degrees between the tails.

So, do you like math/s? Me too. Let's work out the horizontal and vertical tail volume coefficients (Vh and Vv) to see if they're any good.

These are worked out using the following formulas (http://www.eaa62.org/technotes/tail.htm):

Vh = Sh x Lh / Sw x MAC

Vv = Sv x Lv / Sw x b

Plugging in my numbers gives me a Vh of 0.41 and a Vv of 0.031.

My question is: do you think I've chosen the right sized tail? Does it need to be bigger/smaller?

Thanks for taking the time to look through this post. Please note that given the restrictions of my build I can't move the tail backwards so can't increase Vh or Vv that way. I also can't move the wings forward.

Thanks again and any advice would be much appreciated.

Tom

#### Replies

• Absolutely. Stick a rocket on a barn door and it'll fly for too. The engineering comes in when one tries to optimize the design to make it work well and efficiently.

Andy Little said:

It is all very subjective. On paper to my eyeball the tail looks too small if it is that close to the wing. However if that is a problem, you can use a smaller tail if you select a wing section for your main wing whose  "moment coefficient is close to zero"

http://www.mh-aerotools.de/airfoils/foil_flyingwings.htm

A simple way to make such an aerofoil is to apply a bit of up trim to your wing control surfaces.  By this means ( by adding yet more up trim) the horizontal tail area could be theoretically reduced to zero as is the case for a flying wing

The overall point I am trying to make is that ultimately anything can be made to fly and, to get something that feels right after doing your calculations, there is probably no substitute for iterating through several designs or trying different tails to see what works in practise.

EDIT. Note that a smaller tail will result in a model that is more critical re C.G , as I think is pointed out in one of your links

EDIT : edited a few times!

• Perhaps you might want to do some flight testing?

I'm also designing a UAV while keeping in mind modularity which makes it extremely easy to make modifications with minimal cost. For example, a carbon fiber tail boom tubes and be shortened if the airframe is found to be too stable. Getting a longer tube will make it more stable and all that is needed if more or less switching out tail booms. For my design, shifting wing position fore and aft is also a fairly simple task and requires no redesign of the fuselage or the wing.

This sort of designing ideology is especially beneficial to those of us without access to CFD and other advanced stability analysis software.

• Developer

It is all very subjective. On paper to my eyeball the tail looks too small if it is that close to the wing. However if that is a problem, you can use a smaller tail if you select a wing section for your main wing whose  "moment coefficient is close to zero"

http://www.mh-aerotools.de/airfoils/foil_flyingwings.htm

A simple way to make such an aerofoil is to apply a bit of up trim to your wing control surfaces.  By this means ( by adding yet more up trim) the horizontal tail area could be theoretically reduced to zero as is the case for a flying wing

The overall point I am trying to make is that ultimately anything can be made to fly and, to get something that feels right after doing your calculations, there is probably no substitute for iterating through several designs or trying different tails to see what works in practise.

EDIT. Note that a smaller tail will result in a model that is more critical re C.G , as I think is pointed out in one of your links

EDIT : edited a few times!

Airfoils for Flying Wings and Tailless Airplanes
• Usually the volume coefficients are used as an input not some percentages of the wing area. There coefficients you arrived seem ok to me, but they really depend upon how you would like the plane to behave. There's an article in the RC Soaring Digest by Mark Drela explaining the selection of the coefficients.
• Moderator

I always err on the larger size with empennage, as the benefits of bigger outweigh the detriments IMO.

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