An interesting approach (taking advantage of the octagonal shape)!
In my sad and simple case, I just take a picture of the front wheel when I know it’s straight and perpendicular to the axis of the camera POV. I then turn the wheel a bit and shoot the image again. The wheel cover is easy to measure in the resultant images and it is almost perfectly circular. A rough estimate (say, +/- 10 degrees) is fine.
When the picture of the stop sign is flat and straight on, it is 50 feet away. The vertical sides of the octagon are about 9.94 inches if the whole is 2 feet across. When the sign rotates 90° then the near side is 9.94 inches closer than before, thus appearing slightly larger to the camera. (And consequently, the far side will appear smaller - perspective at work…)
at 50 feet, 9.84 inches spans 0.9397° whereas at 49’ 2" it spans 0.9556° (Sin-1 height/distance)
I’m guessing the resolution of the camera is more important than the perspective distortion.
One unfortunate thing here is that, for small angles, small errors in your measurement will result in large errors in angle. For instance, if the wheel is close to straight on, then an error of only 1.5% in your photographic measurement would result in that ±10º error you’re looking for in the wheel angle.
On the other hand, if you’re just trying to tell the difference between a wheel turned 30º and a wheel turned 40º, then you’re probably fine.
Yes, I’m not trying to do a wheel alignment using a camera. The question might simply be, “Are the front wheels cut to the curb in this photo? Or, are they pointed basically forward?”
OTOH, I don’t see how an error of 1.5% yields a difference of 10 degrees. It appears to be around 3 or 4 degrees. In any case, I think that +/- 5% will work fine for me.
arcsin(1.0) = 90 degrees
arcsin(0.985) = 80.06 degrees (or 99.94 degrees)
OK. Typical values I have seen in some preliminary photos have been in the 0.9 range (horizontal/vertical).
Yeah, the difference is less if it’s already angled to start. Taking your example:
arcsin(0.9) = 64.16
arcsin(0.9*0.985) = 62.44
So a <2 degree difference in that case.
Thanks for those comments. Enlightening. I keep telling my wife I’m not a rocket scientist, but she has stayed with me anyway.
Yeah, that’s why I included the qualifier “for small angles”.
Error propagation is tricky, with trig functions. I would recommend that you figure the minimum and maximum possible value for your photographic measurement, and calculate an angle for each of them, and then you’ll know that the true angle is somewhere in between those. If both the minimum possible angle and maximum possible angle are close enough for your purposes, then you’re fine. If they’re not, well, at least you know that, and know that you’ll have to try something else.
Speaking of wind and stop signs - We’ve all seen signs oscillating(?) in the wind during hurricane reporting. Is there a maximum frequency or, if the wind was strong enough, would they just appear as a blur?
Not an aerodynamicist, but my understanding is that there are two possible general issues. You get vortex shedding aka vortex induced vibration, where, the vibration is controlled by the torsional stiffness of the structure - here the sign twisting on its pole and the rate at which vortices are shed from the edge and then swap sides.
Flutter probably is less an issue with vibrating signs, but maybe as the wind gets really strong flexture modes of the plate come into play and the sign starts to flutter. That is like dominated by the period of the flexture mode.
VIV is going to be dependent on the air velocity to the extent that the time to develop and shed the vortex will decrease with wind speed. But it is a coupled system so it isn’t going to be a simple linear relationship and when you get to hurricane speeds the regime may move out of a simple incompressible flow and get properly messy.
As Horace Lamb was famously quoted:
I am an old man now, and when I die and go to Heaven there are two matters on which I hope enlightenment. One is quantum electro-dynamics and the other is turbulence of fluids. About the former, I am really rather optimistic
Also not an aerodynamicist.
The flow field in the lower few dozen feet of a hurricane is insanely turbulent. So any periodicity our sign’s oscillation might exhibit in a uniform e.g. 100mph flow will be overwhelmed by the wild and aperiodic swings in azimuth and speed of the impinging wind field. Agree that VIV is far more of a factor than flutter given the flat-plate area and stiffness of typical road signs.
ISTM that viewed from the right angle in bad enough light an oscillating sign might appear as a blur. For awhile before breaking off. The torsional stiffness of the support post in essence sets an upper limit for how fast the sign can oscillate. Faster than that and the post just tears and the sign goes tumbling merrily downwind like a 150mph buzz-saw blade…
Yes, I know this has no effect on your proposed question, but where else am I going to have any excuse at all to post this?
Stop signs are 30" between opposite sides of their octagon. Unless they are on a high speed road or there is some reason that they are harder to see. Then they are 36".
Submariners in (at least) WWII used a technique almost exactly as described by the OP to estimate relative direction of a target ship seen through a periscope. If it appeared to be full length, then you were directly on the target ship’s beam. If it was half length (and other visual cues), then it was turned 60 degrees away from you (or toward you), etc.
I think it was the book Wahoo, by Richard O’Kane, in which his exercises of using trig to estimate relative target course are described in detail. The guy at the periscope, XO O’Kane in this case, simply had to understand trig.