# Lift equation for elevator and rudder of a plane?

1. Nov 18, 2014

I know that the lift equation for a single wing is L=Cl*0.5*A*r*V^2 where L is lift, Cl is the lift coefficient, A is the area, r is the air density, and V is velocity. Does this equation still apply to the elevator and rudder of a plane or is another equation used? If so, where can I find graphs of the lift coefficients of these parts?

2. Nov 18, 2014

### Staff: Mentor

It ceratinly works for any airfoil. For graphs, you'd probably have to google for the airfoil sections they use. Not sure if that is readily available information.

3. Nov 18, 2014

Also, how accurate is the equation at large angles of attack such as 45 to 90 degrees? I am making a simple plane simulation and I want it to be accurate.

4. Nov 18, 2014

### Staff: Mentor

Angles of attack that high aren't really "flying" and so they aren't typically tested that high. So I'm not sure you'll get a lift coefficient in such a condition.

5. Nov 18, 2014

### rcgldr

Unless the elevator is a stabilator (all moving tail), then the stabilizer consists of a horizontal component and the moving elevator, and the combined surfaces act as a bent airfoil. The rudder situation is similar. The "polars" (lift and drag coefficients versus angle of attack versus Reynolds number) may be available (someone had to know this when designing the aircraft). I don't know if an polar program like XFOIL can model "bent airfoils".

6. Nov 18, 2014

### SteamKing

Staff Emeritus
Most airfoil shapes used on aircraft will 'stall', i.e. lose the ability to provide lift, when the angle of attack reaches about 15 degrees. If a wing stalls when the aircraft is taking off, for example, there is usually insufficient altitude to maneuver the aircraft to recover from the stall and a crash results.

7. Nov 18, 2014

### Staff: Mentor

I would think it is similar to a regular wing with flaps:
http://scilib.narod.ru/Avia/DAC/images/fig068.gif [Broken]

Last edited by a moderator: May 7, 2017
8. Nov 19, 2014

It seems, from the left graph, that the lift coefficient can be approximated by basic section + elevator angle * constant. How accurate would this be? Also, once I translate my simulation from 2d to 3d, how will I deal with the slide slip? The relation would probably be complex. Would it be better to neglect slide slip in my calculations?

9. Nov 19, 2014

### rcgldr

Using a linear equation should be ok as long as the deflection is kept sufficiently below the point where the plot starts to curve.

The graph polars are for a slightly cambered airfoil, since positive lift is produce at zero angle of attack for the plain airfoil. Since the graphs show a higher coefficient of lift for a flapped airfoil at zero angle of attack, it would seem that's there's some fixed angle for the flaps, but that angle is not mentioned. For the stabilizer, you may want a bit of downforce for the plain airfoil at zero angle of attack, assuming this reduces drag. For the rudder, you'd want zero lift at zero angle of attack.

Side slip (rudder) or pitch slip (elevator) would require including the effects related to the fuselage of an aircraft, which could get complicated.

10. Nov 19, 2014

### montoyas7940

Check out flight gear. It is an open source simulator and might give you some ideas.

11. Nov 19, 2014

Should I neglect slide and pitch slip since it it may be difficult to implement? I heard the effects are small.

12. Nov 20, 2014

### elmecheng

When I was studying aircraft design we used xflr5 which has xfoil built in. It's a simulation software. What you are asking isn't a good idea to use just one lift equation because your answer will be wrong and here is why:

1. There are many airfoil shapes with lift data such as a lift coefficient. When you extrude a wing from an airfoil it's data changes a lot. It adds a third dimension that you have to compensate for.

2. There are also 2 main theories to aproximate wings based on what is called the aspect ratio, AS, which is the ratio between length and surface area.

3. You talked about a simulation. This requires ranges of ∝, angle of attack, when this changes the airfoil lift coefficient changes and the wing coefficient changes as well. I highly recommend writting a program to calculate for you or use software. Note: Coefficient of lift also changes with altitude and mach speed

4. You can model them separately as individual wings but when combined in a tail configuration there are vortex effects at the corners, tips, and disrupted flow from the aircraft body. These are not easily calculated by hand.

As for "slipping" effects, I believe you mean viscous effects. At subsonic speeds it can be ignored and often time is. Now, transonic and supersonic speeds can be an issue. When supersonic the lift actually increases a lot due to the viscous effects.

Depending on the scope of your analysis you can simplify and ignore points that I mentioned but I'd have to know the full scope in order to tell you which.

That's not exatly true. Jet fighters, or other high performance aircraft, are designed for large angles of attack around 30° and are capable of going vertical mid-flight. They can only due this because of the massive thrust to weight ratio. I believe takeoff angle is over 25° for aircraft carrier launches which is about a 27-30° aoa for the wings depending on tilt of the wing.