OT: Physics question, calculate speed of a moving car

[chenick]

It's been a while since I've done any kind of physics questions, so excuse my ignorance 🙂
The blur trails in the attached photo (from RFF book 1!) caught my attention and got me thinking (unsuccessfully!)
Would it be possible to calculate the speed of the moving car in the photo?

More info - camera was an Olympus 35 SP, probably taken at 1/30
I was wondering if the trails were related to the street lighting (50hz electricity here)

Just a random thougtht that's been bugging me!

Thanks!

Nick

 

[trittium]

I am an engineering student who took physics 2 years ago, so here are my thoughts. The problem is knowing the length of the blur. If you knew the distance from the car to the lens, and the lens to the film, you could measure the length of the blur on the negative, and use similar triangles to determine the length of the actual blur. Assuming you could do this, all you would need is the shutter speed.

In Math Terms:

velocity= distance / unit time

distance = how far the car moved while the shutter was open = actual length of blur

unit time = shutter speed

substitute variables...

v= actual length of blur / shutter speed

Rules of similar triangles in concordance with Optics:
http://www.gunn.pausd.org/~cbakken/p1A/optics/obookshelf/cvreal2.html

 

[wyk_penguin]

I would rather measure the length of the white spot (head lights?) on the left, which is about 1/9.5 of the frame. The car would have travelled that far in 1/30. Then you would have to factor in enlargement ratios. For that you would need to guess the distance between the camera and the car. Since you know it has a 42mm lens, you can triangulate the actual horizontal distance represented by the frame. Then you could get the speed of the car.

I don't know if you could calculate the speed by the ghost images. Since a 50Hz mains source would cause a filament lamp to go dim(does go out, just get a bit dimmer) 100 times per second. But I don't know about halogen/mercury vapour/sodium vapour street lamps. If a lamp goes dark 100 times a second, it also lights up 100 times a second, so in 1/30s you could get at most 5 images (the first and last being a bit dimmer), but I think I see more than 5. Anyway, if it is indeed 50Hz a.c., the seperating between the images would be the istance travelled in 1/100s. The images could yield the speed, but you would still have to go through estimating the distance between the car and the camera. However the images would be a big help in precisely finding the shutter speed.

Strange that I haven't seen such inages in my long exposure shots. I usualy is just a blur.

p.s. The above may not be suitable for curtain shutters as the frame is usually exposed one part at a time. But for leave shutters, it is OK.

 

[chenick]

Thanks for the suggestions!
Good thinking about the street lights... I think the main light on the car is reflected from the halogen spots (IMO) from the building behind.

Also it is a crop of a larger image, non-cropped version is here:
http://www.rangefinderforum.com/photopost/showphoto.php?photo=735&cat=3322

-Nick

 

[Finder]

The answer is yes and the ways of doing it are many. Another way is if you know the distance between the front and rear lights, you can simply take measurements off the image and calculate the speed based on the shutter speed and the change in the image of the car lights. The accuracy would be related to the accuracy of your shutter speed and measurements.

In technical/scientific imaging, streak photography uses image motion to determine things like velocity. Since streak photography is a continual measure of a period of time, it can reveal more than the usual high speed filming - if a normal high speed film takes 100 frames a second, and a bullet in flight revolves at the same rate, the film makes it appear the bullet does not revolve. If a point can be highlighted on the bullet, a streak photograph can show the revolutions of the bullet.

 

[pvdhaar]

The answer isn't yes, it's "it depends"..

Even if you can work out all the lengths and distances from the image, you still wouldn't be able to tell whether the car moved at a continuous speed. It may be accelerating, or it may be braking. You just can't tell.. I bet you even have a hard time deciding whether it's going forward or backward.

 

[Finder]

Peter, you could determine if there was a change in velocity with a sophisticated densitometer. The intermittant light of the steet lights would also provide a clue. The direction may also be determined - hard to know in the posted image, but the car is travelling on a wet road, but granted that is a long shot. If the speed is relatively fast, you may be able to surmise the car could not be driven in reverse as well. And finally, you can ask the photographer.

 

[Dracotype]

The answer isn't yes, it's "it depends"..

Even if you can work out all the lengths and distances from the image, you still wouldn't be able to tell whether the car moved at a continuous speed. It may be accelerating, or it may be braking. You just can't tell.. I bet you even have a hard time deciding whether it's going forward or backward.

Good point. I still like the idea of measuring the streak of light. Since you know the time it took, and indirectly the distance it traveled, you could calculate its average speed. You could probably even make a pretty good estimate just from the picture. Compare the distance traveled to some known length in the picture. Say the length of the tires. Gauge the length of the tires, and compare with the light streak. There you have it.

The other doosey of a problem is deciding whether the camera is the object that moved or not... inertial reference frame and all that. 😀

But as for the light streak, if the car were moving forward, the streak would project along the car body, showing that the lights had moved farther forward relative to the origianl position. If it had moved backward, the light streak would be in front of the car.

Drew

 

[pvdhaar]

The other doosey of a problem is deciding whether the camera is the object that moved or not... inertial reference frame and all that. 😀

Given that we have day and night, you'd have to factor in up to 1670 kmh that your frame of reference is rotating. But of course that's negligible compared to the 105000 kmh that we're scooting around the sun with, let alone the 800000 kmh or so that the sun is blasting around the galaxy..

Hmm, all far in excess of any reasonable speeding limit, and looks like we need law enforcement on galactic scale..

 

[jaapv]

With a focal plane shutter, wouldn't the speed of the shutter-curtains influence the length of the light streak, especially if the exposure time were shorter than the flash-synchronising speed (being the shortest time that the whole frame is exposed at once)?

 

[Pherdinand]

If the shot would be colour, you could use Doppler to calculate the speed😀 yet another disadvantage of black and white photography.
Also, i recall a sci-fi short story from the end of the 19th century, where they photographed a star moving faster than the speed of light, and they figured it's moving faster than the speed of light from the photo that showed not a cntinuous streak of light but distinct spots.
But this cannot be the case here, since the lamp of the car moves together with the car, and that leaves a continuous trace. Hm hm.
The flickering of street light is however something i never have seen, and i, honestly, don't believe that they flicker. If there was a neon somewhere and that's what illuminates the car, then it is possible.

Finally, it is all a matter of unit of measures. You can easily calculate the speed of the car if you don't need the conventional units. E.g. you can calculate it in frame width percentage per shutter time, instead of km/h or mph. Or, as heard before, in tire width per shutter time.

 

[Pherdinand]

Oh one more thing. Maybe this was a stroboscopic experiment: the car went back and passed exactly the same path with the same speed. This way the shutter speed can be much much shorter (or the car much much faster) giving the fake feeling about its speed! This is a trick that can be used to measure highly reproducible very fast physical phenomenae (like femtosecond magnetization dynamics) incase anyone cares abut them🙂

 

[jaapv]

Of course, Einstein teaches us that the speed of the car is slower for the driver than for the observer, due to the distortion of relative time. Hey! I just found a new defense for speeding tickets!😉

 

[Pherdinand]

There is an anecdote about a guy who passed on red and was stopped by the police. He found the excuse that due to the Doppler effect, at certain speed red seems to be green from the moving car. However the cop was good enough in physics to calculate that he was speeding with a few hundred thousand km/s so he gave him a speeding ticket.

EDIT: ok, it should be about quarter of the speed of light (25.7%), to go from 650 nm red light to 500 nm green...

 

[jamiewakeham]

I use that one regularly with my VIth form students, Pherdinand. Especially if you don't mention the speeding, but just say that the driver claimed to have seen the light as green (and then ask why he was arrested, and what the magnitude of his offence was) you really get to see which of your students are actually awake!

Jamie

 

[Pherdinand]

are you a physics teacher?

 

[jamiewakeham]

Yep.

Jamie

 

[jamiewakeham]

OK, here's a back-of-a-fag-packet estimate. The car length on my screen is about 140mm, and the length of the light track is 17mm.

I'll assume that: the lights are a point source; the camera has not been panned during exposure (background doesn't show this); and the car is 4m long.

So the scale of reproduction is 140:4000, or about 1:28. Therefore, in real life, the lights travelled 17mmx28 or 486mm.

486mm in 0.033sec is 14.7 metres per second.

This is 53kph, or about 32mph. Which is exactly what we'd expect for a car travelling in the middle of a city 🙂

Hey - physics works!

Please feel free to destroy this argument on the grounds of any of my assumptions or mismeasurements.

Jamie

 

[pvdhaar]

I use that one regularly with my VIth form students, Pherdinand. Especially if you don't mention the speeding, but just say that the driver claimed to have seen the light as green (and then ask why he was arrested, and what the magnitude of his offence was) you really get to see which of your students are actually awake!

Jamie

Yeah, but if you accept that the Doppler effect exists, and that the quantum energy of the light is proportional to the wavelength, then where does the energy difference come from? 😉

 

[wyk_penguin]

With a focal plane shutter, wouldn't the speed of the shutter-curtains influence the length of the light streak, especially if the exposure time were shorter than the flash-synchronising speed (being the shortest time that the whole frame is exposed at once)?

I believe the Oly has a leaf shutter. Hence the speed of the shutter is much greater than that of the exposure. So, we would be in the ball park. But yes, a focal plane shutter would add difficulty. :bang:

the driver claimed to have seen the light as green (and then ask why he was arrested, and what the magnitude of his offence was)

If you are talking about Doppler Shift... 😀
Assume red light has wavelength 450nm, then its frequency is 2.2x10^6 Hz; green light on the other hand is about 600nm which is 1.7x10^6Hz. Doing the Math, he would be travelling at 2/3 the speed of light... 😱

Hey - physics works! <-- Reminds me of Prof. Walter Lewin 😀