Forum: Off-topic

Has anyone here taken aerodynamics? Might you be able to help me?

I own the book Aircraft Design: A Conceptual Approach by Dr. Daniel P. Raymer. In the book, he lists equations for initial tail area estimation. The equation for estimating vertical tail area is given as:

Vertical Tail Area = (Vertical Tail Volume Coefficient x Wing Span x Wing Area)/(Moment Arm)

When I was using this equation to predict the tail size for a custom-designed aircraft, the area it gave looked unusually small. In order to check myself, I decided to do some calculations for a real world aircraft and see how well it matched up. I chose to use the F-104 (which bears a similarity to the configuration of my custom design.

Here's what I've calculated:

Vertical Tail Area = (0.07 x 6.63 meters x 18.22 square meters)/(5.094 meters)
Vertical Tail Area = (8.455902 cubic meters)/(5.094 meters)
Vertical Tail Area = 1.66 square meters

The tail volume coefficient was taken from the book which stated that the typical coefficient for a fighter was around 0.07. The wing span and wing area were taken from Wikipedia. The Moment Arm was estimated from a 3-view schematic.

The actual tail area of the F-104 was estimated (from the same schematic) as being around 4.53 square meters. This is more than 2.7 times the estimated required tail area! Not only that, but the book says that a T-tail can have a volume coefficient reduced by about 5% due to the end-plate effect of the horizontal tail. This would equal a tail area of about 1.58 square meters. This makes it off by a factor of almost 2.87! I do realize that using a schematic to do calculations can be a bit off because schematics are often not perfect. I also know that actual aircraft will have tail areas that differ somewhat from calculated predictions due to different real world factors. However, I would have assumed that it should at least be in the same ball park. If the error was something like 0.8 or 1.2, I could understand. A factor of 2.7-2.87, however, seems extreme.

I seriously doubt that Dr. Raymer, who worked for Rockwell International and was involved in the design of their ATF proposal, is at fault here. I'm assuming that I did something wrong.

Any ideas?

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Kryptid,
Using your numbers, the VT volume coefficient is (4.53/1.66)*0.07=.19. I did a quick estimate for the F-16 and got VT volume coefficient = 0.17. So it seems to me the good Dr, is wrong in saying it is 0.07. Perhaps his number is for low speed airplanes, but clearly for high performance, more VT is needed.

I found some other reference for tail volume coefficients, and they were very small, around 0,02 to 0.04, for 100 - 150 kt light planes.

So, I would say use a coefficient appropriate to the airplane you are designing.

Thanks. I'll probably try to measure some appropriate coefficients on other aircraft.

Supersonic aircraft need more vertical tail due to the aftward shift in the center of pressure (reduces the moment arm significantly). VT has to be bigger for supersonic AC. That's why many have twin tails (Tomcat, Eagle, Hornet, Raptor...)

The aft shift creates a longer moment arm, so one might think that would make a tail more effective. But that same aft shift causes the swept tail to twist the wrong direction, thus reducing its local sideslip angle and effectiveness.

The newer jets (Hornet, Raptor, Lightning II) have their tails moved forward to make them more effective at high angle of attack. However, that shortens their moment arm, meaning their area must increase. Look at the huge area required for the Raptor tails. Another interesting development is the PAK-FA all-moving vertical tails, which can be very small due to their moving surface. I suspect they may not be as effective at very low speed and high AOA, which usually determines the tail area requirement.

Forum: Off-topic

Tail Area Calculations