Need to add elevator downforce to total lift when sizing wing area?

Question

Do I need to add elevator downforce to total lift when sizing wing area?

Say a small airplane weighs 1,000 lbs, and both the wing and elevator have a max Cl of 1.5, and my elevator is 20% of my wing area, so max elevator downforce is roughly 20% of 1,000 lbs or 200 lbs in a classic configuration.

Doesn't the main wing then have to carry 1,000lbs + 200 lbs negative elevator lift, for a total lift of 1,200 lbs?

If the plane is in a tandem configuration, the main wing would only have to carry 800 lbs, as the elevator has 200 lbs of positive lift,for a total lift of 1,000 lbs.

1,200/800 lbs is 150%!!, so if I use the tandem configuration, my main wing can be 50% smaller!!! Is this correct?

Answer 1

No.

First, your horizontal tail will need some control margin. A trimmed state where it flies close to c$_{l_{min}}$ is a grave design error. Next, your horizontal tail sees the same angle of attack change as the wing, reduced by downwash. This means that the strongest downforce is trimmed in fast flight, when the angle of attack is small. Fly slower and angle of attack rises not only on the wing, but also on the tail. Chances are that your tail produces positive lift in slow flight.

Flaps will change this picture slightly. Setting flaps will need you to re-trim the aircraft because now the center of the wing's lift has moved slightly backwards, so the load on the tail becomes more negative.

Fun fact: If you have a symmetrical wing airfoil, the trimmed tail load will be constant over the whole envelope. In order to achieve the best control power, this tail load should ideally be zero.

Now for the tandem wing: You assume that now both surfaces create lift, so overall drag should be lowest. But adding area on the tail will reduce the needed wing area. Given that the planform shape stays constant, less area means less wing span. However, induced drag is proportional to the span loading, and a lower span will mean more induced drag. Therefore, a conventional design with an unloaded tail of minimum size will have the lowest drag.

Answer 2

Your description would apply to a situation where we have an all-moving horizontal stabilizer (simpler to consider than the elevator case) with an airfoil the same as the wing but upside-down, flying at a negative (downlifting) angle-of-attack that is exactly equal and opposite to the wing's positive (uplifting) angle-of-attack. In practice you would never have a horizontal stabilizer flying at this strong a negative angle-of-attack and creating this much downforce. But yes, if the CG were so far forward that this much downforce were needed for balance, the situation would be as you describe, and this would definitely add a great deal to the total lift that the wing would have to generate.

So the basic answer to your question is "yes", but you have chose a very extreme case of a downlifting tail for your illustration. In practice it can be shown that a configuration with a slightly-downlifting tail is generally more efficient than a configuration with a strongly uplifting tail.