Originally Posted by
bentwings
A number of us gathered with social distancing to talk about scale models. Almost the first topic was scale speed it turned into a shouting match as we tried to maintain the distance and keep tempered in the aneling range. So assume we are watching an F8F Bearecat practicing for the Reno air races. He flies by at 500 mph or 4000 feet per second. One of the guys has a 1/4 scale model of the plane. How fast in real world terms does this model have to fly at to represent scale speed?
Interesting problem. My approach:
- Approximate problem by imagining an observer is standing at middle of circle of radius "R" (in feet)
- Full scale plane has length "L" (in feet)
- Full scale plane flying at speed of "X" (in feet per second)
Knowns:
- Distance along circumference of a circle S = Radius * Angle (in radians)
- Angular velocity, in radians / second = Velocity along circumference in ft/sec divided by Radius in feet
- An object of length L at a distance of R subtends an angle (to the eye) = 2 * arctan[(L/2)/R]
So now it's an issue of deciding your distance and speed for the full scale plane, then calculating at what distance a model 1/4 size subtends the same angle to the eye and travels at the same angular velocity (to the observer). As it turns out, the distance is scale factor times distance from full scale observation. Same for speed.
So an F4U Corsair flying at 400 mph on a circular path of radius 5280 feet around the observer. For a 1/4 model to appear the same, it has to be at both 1/4 the distance AND 1/4 the speed.
Another way, a 1/8 scale turbine model of an F/A-18C 500 feet away from the observer travelling at 200 MPH would appear the same as a full scale Hornet 4000 feet away at 1600 MPH. With the ground and plane visible to the observer for the model, the relative velocity doesn't look right because you don't see many Hornets that close to the ground going that fast.