The choice of sweep angle (low speed) and its impact on C_L, C_D, C_M

[Leo Liu]

My school's group project is to design a powered model flying wing that can fly for as long as possible. To make it stable in the longitudinal direction, we either have to use a swept wing design or an airfoil with reflex (like BR1). We are forced to use wing sweep because the airfoil with reflex cannot create enough lift.

A rule of thumb I found for the sweep angle is about $20^\circ$ for a model flying wing. I am not sure if it is optimal and am keen to know if there is a way to treat this topic more rigorously.

I did some research and was not able to find a rule-of-thumb formula for $C_L$, $C_D$, and $C_M$. The closest thing I can find is this research.

I am wondering if such a formula exists, and if not, how we should estimate the changes in the three coefficients. Do we just apply a guessed margin and call it a day?

Another question I would like to ask is what are the factors and influences we need to consider when deciding the locations to mount the motors and propellers. Would it be more beneficial to put them at the leading edge or at the trailing edge?

The initial design of our flying wing:

Your input will be highly appreciated. Have a good one!

 

[Baluncore]

I am wondering if such a formula exist, and if not, how we should estimate the changes in the three coefficients.

The stability comes from flying slightly sideways, when one wing appears to become longer with a shorter chord, while the other becomes shorter with a longer chord. The surface area of the wing remains constant, but the lift and drag stabilise the orientation of the wing to the direction of flight.

Another question I would like to ask is what are the factors and influences we need to consider when deciding the locations to mount the motors and propellers. Would it be more beneficial to put them at the leading edge or at the trailing edge?

Avoid disturbing airflow over the upper surface of the wing, which is where most of the lift is found. That suggests mounting the propeller below and/or behind the wing. Make sure the orientation control surfaces (equivalent tail) are in the propeller-stream, so you will have directional control when on the ground, or when flying at just above stall speed.
The mass of the motors will determine CofM. The aircraft should be stable in glide, so mounting engines near the centre of the wing is preferred, but not ideal. A longer prop drive shaft is a possibility.

 

[Leo Liu]

Thanks for the answers.

The stability comes from flying slightly sideways, when one wing appears to become longer with a shorter chord, while the other becomes shorter with a longer chord. The surface area of the wing remains constant, but the lift and drag stabilise the orientation of the wing to the direction of flight.

By stability I actually meant longitudinal stability rather than directional. From my understanding the wing sweep shifts the lift behind the CoM, but I don't quite understand how this works without reflex which creates a positive moment about the aerodynamic center. Simulation indicates stability for the design with NACA2412. (We also came up with a hybrid design involving both types of airfoils to get the advantages of both, but the lift performance is worse than NACA2412.)

The mass of the motors will determine CofM. The aircraft should be stable in glide, so mounting engines near the centre of the wing is preferred, but not ideal. A longer prop drive shaft is a possibility.

Sorry by center do you mean the aerodynamic center or CoM? And why does mounting the engines near the center of the wing ensure that the plane glides well?

 

[Baluncore]

Following loss of power, you need to recover the craft by gliding. The aerodynamic balance at a stable low-speed glide should be optimised. Under power or in a fast glide, you will have energy to waste and a faster airflow over the control surfaces, so efficiency is not critical. (You are not designing this craft for long haul passenger transport).

If you mount the engines towards the rear, with pusher props, you must then add mass up front to counter the moment about the aerodynamic centre. That added mass is a waste of good lift if you can avoid ballast.

You have not identified the type of engine, electric or liquid fuel.

Stability is improved if longitudinal inertia is increased, if the mass can be distributed towards the ends of a longer body. Engines at the back with batteries up front might work, but since the mass of fuel is changing during the flight, fuel tanks must be in a neutral position in the wing. That explains why heavy engines are hung below the wing in many aircraft.

 

[Leo Liu]

Following loss of power, you need to recover the craft by gliding.

If the flights of our model plane are designed to be powered throughout, will it change the requirement here? We don't want to waste energy by making the plane climbing up.

You have not identified the type of engine, electric or liquid fuel.

The wingspan is a mere 600mm so we can only use two coreless DC motors to power the flying wing.

Engines at the back with batteries up front might work, but since the mass of fuel is changing during the flight, fuel tanks must be in a neutral position in the wing.

Hmmmm our plane will use a battery. I assume I can place it at the front as a counterweight?

 

[Baluncore]

our plane will use a battery. I assume I can place it at the front as a counterweight?

Yes. A battery will make a good counterweight.
The two motors can be spaced apart, at the trailing edge. If they are far apart they will provide directional control, and some stabilising inertia.

Contemplate having two counter-rotating pusher propellers, one in each wing tip vortex. That way, you might recover some of the induced drag as thrust.