Trying to determine initial thrust on an object from angular velocity?

Hi all,

I built an electric paper airplane launcher and I'm trying to figure out how much force or thrust is being applied to my paper airplane when it's launched. The setup looks like this:



The discs are 124mm in diameter, are spinning at approximately 5800 RPM each, and are about 1mm apart (far enough not to touch but close enough to grab the airplane. The airplane is 7 inches long. I'm trying to figure out how much force is transferred to the airplane.

My initial guess was to convert the angular velocity of the discs into linear velocity, and multiply that by mass of the plane.. but I don't think that's accurate.

First, I'm not sure that two discs spinning in opposite directions at 5800 RPM each equals an angular velocity of 11600 RPM. I'm not sure that I can combine them that way.

Second, assuming that I figure out the combined linear velocity of both discs, I am not sure how that is transferred to the airplane. The discs are applying force to the airplane for the total distance of its length, but I'm not sure how that factors into the airplane's initial acceleration.

I'm sure there is a lot I'm missing here.. just looking for a point in the right direction. Thank you!