My Dad just sent me the following images:
He apparently decided to build a launch platform[1] and some water rockets to enjoy with my niece and nephew who are currently visiting. He said they were getting about 200-300 feet of altitude on 70 psi.
Since I am, after all, a camera geek AND a rocket scientist, I had to do a bit of photo analysis to extract some info from the image. Thankfully, the images my Dad emailed still had the EXIF data intact.
Here’s my analysis in the form of an open email to my Dad and sister. The references, [edits] and emphasis were added by me since the email.
You took the picture on the Canon A520. The [launch] image is full resolution at 2272 pixels tall but cropped horizontally to only 736. The reported focal length was 6mm. The sensor is approximately 5.76×4.29mm.[2][3]
The vertical field of view is calculated to be 51.28 degrees. The exposure was 1/160 of a second long and the fin of the rocket traveled approximately 107 pixels (paint the fins a dark color for better contrast). The cinder block
sin the foreground is about 82 pixels tall. Consideringthat the cinder block is about as far away as the rocket and is at about the same distance from the center of the image. Assuming this is an 8x8x16 block, then 82 pixels equals about 8″. This means the rocket traveled about 10.4″ during the exposure. That’s 1670 inches per second, or 139 fps or 95 mph!Now that’s probably a high estimate because the fins have some height and it’s hard to tell whether I’m measuring someplace where the fins are just a point, or in the middle of the fin. So conservatively, if the rocket only moved 8 inches (2.5″ of blur due to the actual height of the fin), it’s still over 70 mph. (I’d bet it’s closer to the 90 number though as the fins taper to a point based on your other image and the contrast is pretty good.)
I’d be comfortable saying that the point you captured is pretty much the maximum velocity since the solid stream of water ends several feet below the rocket. The wide burst of water a few feet back is probably the remaining air pressure atomizing (in the perfume bottle sense) the last bits of water (think squirt….foom). The area directly behind the rocket is pretty clear, which makes me think the propellant has been exhausted.
Sweet. On the edge of 100mph from a soda bottle and some water. Nicely done Dad.
Some additional musings:
- Although the pointy hat looks cool, the lowest drag would probably be achieved with a semi-spherical nose cone since the speeds are very subsonic. Torpedoes are round because the speed of sound in the medium, water, is VERY much faster than the speed of the torpedo. Same thing goes for submarines, passenger jets and cargo planes.
- You may find that the rounded bottle is actually lower drag than the cone.
- You will probably find that it doesn’t make much difference.
- Is there some kind of cylinder in the center of the bottle, or is that just a stand to hold it for the photo?
- Another excursion would be to spike the propellant with salt, sugar or even sand to increase its density. I’d wager that the pop[4] that was originally in that bottle would give you more kick then water… but would be much messier.
- I find myself wondering if there would be a way to baffle the water in some way so that pressure has more time to act on it. If there is still air pressure when the water runs out, then you get the ‘foom’ blowout, which is pretty wasteful. I guess I’m really thinking about nozzle design and/or an exit ‘barrel’ to give the gas more time to work on the fluid (like a rifle).
In any case, it looks like fun.
June 25th, 2009 at 9:06 pm
Best. Grandpa. Ever.