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Q & A: how much to fill bottle rocket?

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Most recent answer: 09/28/2011
Q:
If I am making a bottle rocket with a 16.9 ounce soda bottle, about how much water should I use?
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- Kennedy (age 12)
Bethalto, Illinois United States
A:
I'm not sure exactly how much to fill it, so you will need to do a little experimenting. However, a simple argument says about how much to fill it. 

The energy to drive the rocket comes from the compressed air. (The water doen't compress enough to store much energy.) So you need pretty much of the rocket to be left empty. The forward momentum of the rocket has to just match the backward momentum of the material ejected. Air has so little mass that it can't carry much momentum backward. So you need the heavier water for that. So a starting guess would be to use 1/2 the volume each for air and water, and adjust around that by experiment.

I could get a little more precise, still not trying to do an exact solution. Call the fraction of the volume used for the water x, with (1-x) the fraction for air. The energy stored (at the maximum pressure you can use) will be proportional to (1-x). The mass ejected will be proportional to x. The energy that mass gets if it's ejected at speed v is proportional to xv2. So v2 is proportional to (1-x)/x. So v goes as sqrt((1-x)/x)). The ejected momentum goes as mv, or sqrt((1-x)x)). That make it sound like our guess that the best x=0.5 is right (since it makes x(1-x) as big as possible), but we haven't allowed for the gradual change in speed as the rocket accelerates, etc., so that's just a starting point for your experiments.

Mike W.
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(published on 05/02/2011)

Follow-Up #1: bottle rocket calculation

Q:
I also have to make a pop bottle rocket, i saw that you were talking about having to do a calculation to get the amount of water needed, so how exactly do you performthis calculation?
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- Lucy (age 12)
Canada
A:
I've marked this as a follow-up to an answer that included a crude calculation.

To do a more accurate calculation, you might do something like this.

1. Call the mass of the bottle m, and its volume V. We want to calculate x, the fraction of the bottle's volume to fill with water. The density ρ of the water is very close to 1.0 gm/cm3. So the initial mass is m+ρVx. Call the initial pressure p.

2. You have to figure out how much momentum each little increment of expelled water gives to the remaining rocket, whose mass is the rocket mass plus the remaining water mass. The change in momentum of the remaining rocket is equal to the speed s of the ejected mass in the frame of the rocket.  I don't quite know how to calculate s because I'm not sure how it depends on the pressure.  The pressure drops as the empty volume grows, approximately inversely proportional to volume. (For specialists- I'm using isothermal, although adiabatic may be closer.)

3.   The speed change of the rocket is s*(ejected mass) / (remaining mass)

4. Since the pressure and the remaining mass keep changing, you have to do an integral over little increments of ejected mass to get how the rocket speed changes as the mass gets ejected. You also need to use the changing s to calculate how much mass is ejected per time, so that you can convert that to distance traveled.

So that's the outline. Even this calculation involves some approximations, such as neglecting air friction. You see why I recommended just trying a few different fill levels around the 1/2 filled value. That saves doing a tough calculation and avoids any approximations or forgotten influences in the calculation.

Mike W.

p.s. I tried playing around a little with doing that integral, still using some approximations. It looks like in the approximate calculations for a range of guesses about the weight of the bottle somewhere around 30% filled gives about as good a result as you can get.
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(published on 05/08/2011)

Follow-Up #2: bottle rocket plans

Q:
I was wondering, how many bottles should i use and why, how much water should i put in my soda bottle and also how much air pressure should i use, my science teacher says the maximum we can use is 90 psi. Lastly is it ok if i use duck tape to stick the bottles together
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- Lucy (age 12)
Quebec
A:
Your teacher is definitely right that you shouldn't use over 90 psi. Some people even recommend slightly lower limits. The idea is to make sure the bottle doesn't explode.

We've had a lot of discussion about how much water to use. I did a very crude calculation that gave 1/2 full as a suggestion. Looking around, I see that many people with experience recommend about 1/3 full. The main factor left out of my calculation was allowance for the first water expelled having to lift not just the bottle but also the water that hasn't yet been expelled. Including that would reduce the recommended level below the 1/2-fill found in the crude calculation. So 1/3 full sounds like a good starting point.

The only reason I can think to use several bottles is to reduce the ratio of air friction to rocket drive. I bet that isn't very effective at all, since the air friction approximately doubles as you double the number of bottles.  I'd just use a single big bottle and put a lot of care into making good fins, etc. and into testing everything carefully. This is just a guess, but I bet that works better than fussing with a bunch of bottles.

If for some reason you have to use more than one bottle, duct tape would be ok.

Mike W.
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(published on 05/09/2011)

Follow-Up #3: bottle rocket plans

Q:
what is the best degrees for wings? how many wings should you have on a bottle rocket? Could you use tape on the bottle rocket? how much water should you put in the bottle rocket?
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- cherri (age 14)
kentwood,mi
A:
I've marked your question as a follow-up to others about the best water fill fraction, which we estimate is about 1/3 of the volume.

If you want the wings to be symmetrically arranged (balanced) and to provide stability against wobbles in all directions, you need at least 3. Wings also give some drag, so I would keep it to either 3 or 4.  You could of course use some tape, but if you can get things to hold well enough with glue, that might add less weight. I don't know how to figure the best slope for the wings, so you might just look at what other successful bottle-rocketeers have used.

Mike W.
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(published on 05/24/2011)

Follow-Up #4: big or little bottle rocket

Q:
Is it better to make a water bottle rocket with a large mass or a small mass?
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- Charl (age 15)
Boston
A:
I guess you're asking whether to use a big bottle or a little bottle. Generally a big bottle works better. The propellants provide energy proportional to the volume, but the bottle (with walls of fixed thickness) provides weight proportional to the area. You want a lot of propulsion per weight, so you want a big volume/area ratio. You also want the air friction to play a relatively small role. For both reasons, you want to use a big bottle. You can get more info from old questions, so I've marked this as a follow-up.

Mike W.
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(published on 06/06/2011)

Follow-Up #5: bottle rocket fins

Q:
How many number of fins should be used for 1.5 litr bottle rocket. The number of fin depends on what criteria?
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- shujaat (age 20)
Aurangabad, Maharashtra, India.
A:
I've marked this as a follow-up. It turns out the older answer was hard to find because we followed the question in calling the fins "wings".

Mike W.
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(published on 07/03/2011)

Follow-Up #6: filling a bottle rocket

Q:
Hi in science we rebuilding bottle rockets and it's a contest whoever can make their 2 liter bottle fly the farthest wins!!!!!! Only one problem don't know how much water to put in for it to launch the farthest please reply ASAP launching in 2 days!!!!!thanks
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- Savannah (age 13)
Andover mn usa
A:
Hi Savannah- we don't have much to add to our old answers, which this now follows. Maybe 1/3 full is about right.

Again a reminder- for quick answers, be sure to use our search engine. Often, as here, we've already answered your question.

Mike W.


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(published on 09/17/2011)

Follow-Up #7: filling bottle rocket

Q:
We are building bottle rockets out of 1 liter seltzer bottles in our science class. My partner and I are debating about how much water we should put in the bottle. My partner thinks half full, but I think that is too much water, because we are putting in up to 75 pounds of pressure. How much water should we put in?
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- Shaniqua
A:
We have answered this question several times.   It seems that constructing bottle rockets is a popular pastime.   Type in id=17080 into the main page to get our latest.

Mike W.
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(published on 09/28/2011)

Follow-up on this answer.