ISP of a Bottle Rocket

[dozerman]

Has anybody ever calculated the ISP of a random bottle rocket? Just curious.

[darthgently]

Finally someone has to courage to ask the taboo question!  Following

[Linkageless]

I think Scott Manley addressed the potential ISP of a steam rocket in one of his videos.... 

 

[SunlitZelkova]

What about the ISP of a stomp rocket?

[farmerben]

19 hours ago, dozerman said:

Has anybody ever calculated the ISP of a random bottle rocket? Just curious.

I don't have the equation handy, but it should be possible to calculate if you know the initial and final masses and the altitude it reached.

[magnemoe]

22 hours ago, Linkageless said:

I think Scott Manley addressed the potential ISP of a steam rocket in one of his videos.... 

 

Steam rockets should get an significantly higher ISP or more likely trust as i assume it used super heated water who turn into steam then "fired". Still pretty crappy, fine for launching planes of an carrier as the catapult is stage zero and part of the ship. 

[farmerben]

https://space.stackexchange.com/questions/54476/what-is-the-isp-of-gunpowder-likely-to-be-could-this-table-be-right-can-it-eve

These guys settled on about 90s for the ISP of gunpowder.

[magnemoe]

On 1/10/2025 at 2:04 AM, farmerben said:

https://space.stackexchange.com/questions/54476/what-is-the-isp-of-gunpowder-likely-to-be-could-this-table-be-right-can-it-eve

These guys settled on about 90s for the ISP of gunpowder.

Using model rockets as baseline  Now modern gunpowder is more energetic but its not designed as rocket fuel. 240 s for the SRB is very good. Now that is the ISP of common small to mid sized missiles? I guess around 200 s.  

[farmerben]

Modern gunpowder is made of mostly nitrogen.  Black powder has sulfur and potassium.  The heavier the exhaust the slower it goes. 

[magnemoe]

1 hour ago, farmerben said:

Modern gunpowder is made of mostly nitrogen.  Black powder has sulfur and potassium.  The heavier the exhaust the slower it goes. 

Excellent point, now this does not matter in a gun, but modern gunpowder is more powerful so using same amount of it in an gun designed for black powder would be an bad idea. 

[Franchon]

Let's see, ISP is calculated with the exaust speed (here speed of the water).

Assuming a bottle rocket to be a pressure vessel and the pressure converted to speed at the neck, we can use Bernoulli's equation at each end of the convergent:

V1²/2+gz1+P1/rho = V2²/2+gz2+P2/rho

P1~6barA                  P2=1 barA                     z1-z2=15cm

V1  =  V2/S1*S2  =  V2/10     if we assume a bottle of 8 cm in diameter (1.5L)

So we have :

(V2²-100*V2²)/200 = g(z2-z1) +  (P2-P1)/rho
V2 = 32 m/s

So the ISP of a water bottle is 3 !

But this ISP is decreasing as the volume of air empties out. For a 1.5L bottle filled with 1L of water and 0.5L of air at 6 bar, the pressure decreased down to 2 bar at the end of the thrust, lowering the speed to 14 m/s (ISP of 1.4)

So the average ISP is 2.2

[StrandedonEarth]

28 minutes ago, Franchon said:

Let's see, ISP is calculated with the exaust speed (here speed of the water).

Assuming a bottle rocket to be a pressure vessel and the pressure converted to speed at the neck, we can use Bernoulli's equation at each end of the convergent:

V1²/2+gz1+P1/rho = V2²/2+gz2+P2/rho

P1~6barA                  P2=1 barA                     z1-z2=15cm

V1  =  V2/S1*S2  =  V2/10     if we assume a bottle of 8 cm in diameter (1.5L)

So we have :

(V2²-100*V2²)/200 = g(z2-z1) +  (P2-P1)/rho
V2 = 32 m/s

So the ISP of a water bottle is 3 !

But this ISP is decreasing as the volume of air empties out. For a 1.5L bottle filled with 1L of water and 0.5L of air at 6 bar, the pressure decreased down to 2 bar at the end of the thrust, lowering the speed to 14 m/s (ISP of 1.4)

So the average ISP is 2.2

Terminology is iffy. You’re describing what I know as a “water rocket.”  What I know as a “bottle rocket” is a very small rocket firework (thinking <1cm dia, ~3-4 cm long) attached  to a long thin stick for stability. The stick is placed in an empty (glass) pop bottle for launching, hence the name “bottle rocket”. Which explains why other replies are talking about one kind of powder propellant or another. 

[Franchon]

Ah yes sorry, english is not my native language.

For powder rocket, I guess it depends of the canal shape, I read somewhere that Goddard manages to increase the efficiency of powder rocket using a de Laval nozzle, going from 30s to 200-250 of isp (source)

The 30s rocket was for an old 1 pound ship rocket, which in design is similar to bottle rocket I guess ?

[monophonic]

On 1/11/2025 at 7:47 PM, magnemoe said:

Excellent point, now this does not matter in a gun, but modern gunpowder is more powerful so using same amount of it in an gun designed for black powder would be an bad idea. 

There is a lot more science than that in internal ballistics of a gun. Which goes to say the opposite, using black powder in a gun designed for modern propellants, is an equally bad idea. Like, barrel burstingly bad. But I'm not really an expert on this (either), and we are getting off topic, so I'll leave this at that.