# Help me understand specific impulse

#### James Owen

##### Well-Known Member
So I need some help understanding some elements of rocket propulsion.

Total impulse? Great. Got it. It's like the capacity on a battery - if a 5 amp-hour battery puts out 5 amps, it will die in an hour. Likewise, if a 500 newton-second motor put out 500N of thrust, it would burn out after 1 second. This works in the opposite direction as well; if a motor provides an average thrust of 20N and burns for 2 seconds, it has 40 N-s of total impulse.
Easy. I get this one.

Specific impulse? Uhhh... I know it's got something to do with efficiency... and it's measured in... seconds?

Why do liquid engines have higher ISPs than solids?

How does changing the isp affect the motor performance?

decreasing the total impulse but keeping the thrust constant of a motor will decrease the burn time, while decreasing total impulse with a fixed burn time will reduce your thrust.

If you managed to keep some things constant and changed the specific impulse, how would it change the motor?

Excuse my ignorance,
James

#### Antares JS

##### Professional Amateur
TRF Supporter
Specific impulse is total impulse per unit weight, which gives a unit of force*time/force, which reduces to time, which is why specific impulse is in seconds. A higher specific impulse means you are getting more total impulse per unit of propellant weight, which means it's more efficient.

On a very basic level, solids tend to have lower specific impulse because they are generally more dense and therefore heavier than liquids. Hydrogen has the highest specific impulse possible for chemical rockets because hydrogen is the lightest substance in the universe, meaning the total impulse of a hydrogen rocket engine is divided by the smallest possible weight.

#### James Owen

##### Well-Known Member
Ok, thanks so much. These helped a lot.

Going with my last question about what changing the specific
Impulse would do, I could get a motor of the same total impulse but that uses less propellant (in terms of weight) and therefore has a higher net thrust, even if its thrust curve stays the same.
Does this logic seem right?

#### prfesser

##### Well-Known Member
TRF Supporter
Isp describes the propellant, and it depends on what's in there. Most APCP propellant has Isp around 180-220 seconds. "Sugar" propellant, around 120 seconds. BP, around 80 seconds.

Hypothetical example may help. Two motors, motor A contains 1 lb propellant with Isp=100, motor B with Isp=200. To cut back on variables, both motors are designed for a chamber pressure of 1000 psi, and both have their nozzles designed to give 1 lb of thrust.

Motor A will burn for 100 seconds. Motor B will burn for 200 seconds.

1 lb thrust x 100 seconds / 1 lb propellant = 100 seconds (the lb units in numerator and denominator cancel out.)

1 lb thrust x 200 seconds / 1 lb propellant = 200 seconds

This also means that if the motors are designed instead to burn for one second, Motor A will produce 100 lb thrust and Motor B produces 200 lb thrust.

So a typical APCP-containing motor will produce around 2-3 times the total impulse of a BP-containing motor, given that both contain the same amount of propellant.

Isp can also be expressed in meters per second; exhaust velocity.

HTH,
Terry

#### sriegel

##### Well-Known Member
TRF Supporter
Increasing the ISP would not change motor performance per se, but it would allow you to move the rocket with less fuel mass, allowing you to use a smaller rocket or carry more useful payload.

Moving over to non-chemical reaction thrusters, there are ones that vapirize and ionize diffetent materiala (e.g., Teflon blocks) then accelerate the ions with magnetic or electrical fields to produce crazy high ISPs, an order of magnitude or more compated to chemical rockets. Thus, a few kg of fuel could provide a decade of stationkeeping for a satellite. The tradeoff with these thrusters is they produce incredibly weak thrust, so you don't accelerate very fast. But if you can keep it up for months, you can go a long way for a whole lot less propellant mass.

#### prfesser

##### Well-Known Member
TRF Supporter
Ok, thanks so much. That helps a lot.

Going with my last question about what changing the specific
Impulse would do, I could get a motor of the same total impulse but that uses less propellant (in terms of weight) and therefore has a higher net thrust, even if its thrust curve stays the same.
Does this logic seem right?

Hopefully this figure will help. I'll check with the authors to see if it's okay to post.

The figure also addresses a common misconception, that fast-burning propellant has higher specific impulse than slow-burning propellant; not necessarily true. Two AP propellants could be designed to have the same Isp; propellant "Fast" with an additive to make it burn three times as fast as propellant "slow", giving the results below.

#### Antares JS

##### Professional Amateur
TRF Supporter
Here's a slide I made for a presentation on solid rocket motors a while back.

Bear in mind that BP has a specific impulse of about 80 seconds, and APCP has specific impulse in the high 200's depending on the exact formula.

#### WillMarchant

##### Well-Known Member
TRF Supporter
I liked those last two example images. Do we have a library on the forum of individual MS-PowerPoint slides that we could all share to pick and choose from when pulling together presentations?

##### Well-Known Member
TRF Supporter
There are several mathematical expressions that contain Isp. Another way to look at Isp is that the higher the Isp the higher the exhaust velocity. A simple formula for exhaust velocity (fps) is

Ve = Isp x 32.2

So, the rocket motor exhaust velocity is directly proportional to the Isp. In general the lighter the molecular weight of the exhaust products, the higher will be the Isp (and the exhaust velocity). In general liquid propellants have lighter exhaust products and, hence, higher exhaust velocity and Isp. One way to lower molecular weight in the exhaust products is to have more hydrogen in the combustion products. This is naturally easier to do in liquid propellants.

#### jsdemar

##### Well-Known Member
Lots of excellent replies. I'll add my 2 cents worth.

(From "EX for Dummies", class notes, John DeMar, 1/17/2006)....

Cf: “Thrust Coefficient”, from the nozzle expansion gain. A "free" increase in thrust, total impulse, and Isp from a properly designed nozzle.

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#### mbeels

##### Yes balsa
TRF Supporter
Interesting thread. Is there a similar metric for something like volumetric efficiency for a rocket motor? For example, if two motors (A&B) have the same over all length and over all diameter, and if motor A has a higher ISP than motor B, but motor A has a larger central core diameter (and hence less propellant), motor B may end up with more total impulse.

#### prfesser

##### Well-Known Member
TRF Supporter
Interesting thread. Is there a similar metric for something like volumetric efficiency for a rocket motor? For example, if two motors (A&B) have the same over all length and over all diameter, and if motor A has a higher ISP than motor B, but motor A has a larger central core diameter (and hence less propellant), motor B may end up with more total impulse.
You are correct; a motor with more (but lower Isp) propellant (by virtue of a smaller core) can have lower total impulse than a motor with less (but higher Isp) propellant. Depends on the mass of the propellant and the values of Isp.

We can confuse the issue even more! There's another term, "density Isp". Aerotech's H128W and H238T motors have the same total impulse, 175 N-s, even though Blue Thunder has higher Isp than White Lightning. Reason: WL is significantly more dense than BT, so the 29/180 case holds 90 grams of WL as opposed to 80 grams of BT. WL's lower Isp but higher density gives it about the same density Isp as does BT.

Class dismissed. Quiz on Friday.

#### jsdemar

##### Well-Known Member
Another interesting way to look at "Density Isp" is to consider a rocket's mass compared to the mass of the propellant. What we build in the rocketry hobby, and even the most efficient amateur rockets, are heavier than the optimal mass. By using a propellant with a higher density, the overall mass of the loaded rocket doesn't change significantly. But, the thrust will increase (and generally the total impulse will increase) by using the denser propellant. This is most important when the rocket motor's volume is limited and the payload is very heavy.

In real-rocketry applications, high "density impulse" (propellant density * Isp) is used for ejection seat motors and escape towers, to name a couple. For this purpose, some of the oxidizer is replaced with a "heavy metal" oxidizer. Historically, this was lead oxide (specific gravity ~10), but it's been phased out due to environmental concerns. It's been replaced by another heavy oxidizer with a specific gravity of 8.9. CTI's IMAX propellant uses it.

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#### rocket_troy

##### Well-Known Member
TRF Supporter
isp = amount of bounce to the ounce

TP

#### sharkbait

##### Well-Known Member
Another interesting way to look at "Density Isp" is to consider a rocket's mass compared to the mass of the propellant. What we build in the rocketry hobby, and even the most efficient amateur rockets, are heavier than the optimal mass. By using a propellant with a higher density, the overall mass of the loaded rocket doesn't change significantly. But, the thrust will increase (and generally the total impulse will increase) by using the denser propellant. This is most important when the rocket motor's volume is limited and the payload is very heavy.

In real-rocketry applications, high "density impulse" (propellant density * Isp) is used for ejection seat motors and escape towers, to name a couple. For this purpose, some of the oxidizer is replaced with a "heavy metal" oxidizer. Historically, this was lead oxide (specific gravity ~10), but it's been phased out due to environmental concerns. It's been replaced by another heavy oxidizer with a specific gravity of 8. CTI's IMAX propellant uses it.
I thought it was 8.9

#### James Owen

##### Well-Known Member
Thanks so much everyone! I learned a lot from this! Clears up all of my curiosities, and more! I never knew about density isp or specific gravity or any of that. Thanks!

#### James Owen

##### Well-Known Member
Aerotech's H128W and H238T motors have the same total impulse, 175 N-s, even though Blue Thunder has higher Isp than White Lightning. Reason: WL is significantly more dense than BT, so the 29/180 case holds 90 grams of WL as opposed to 80 grams of BT. WL's lower Isp but higher density gives it about the same density Isp as does BT.
Fascinating!

#### Tom Flint

##### Well-Known Member
Specific impulse makes more sense when you think of it in metric units, in which case it's expressed in Newton-seconds per kilogram. That way it's easy to think of how much total impulse you would get from a kilogram of propellant. Specific impulse in seconds is a result of using the old English units of measurement where it was expressed as pound-seconds of total impulse per pound mass of propellant, shortened to pound-seconds per pound. You can see where the confusion arose because someone then crossed out the pounds in the numerator of the fraction and the pounds in the denominator, leaving only seconds. Pounds force and pounds mass are not really the same thing though and this is why English units suck for engineering, and why specific impulse in seconds is so counterintuitive. But because early rocket engineers used English units, seconds of specific impulse has stuck as the industry standard.

#### jsdemar

##### Well-Known Member
Specific impulse makes more sense when you think of it in metric units, in which case it's expressed in Newton-seconds per kilogram. That way it's easy to think of how much total impulse you would get from a kilogram of propellant. Specific impulse in seconds is a result of using the old English units of measurement where it was expressed as pound-seconds of total impulse per pound mass of propellant, shortened to pound-seconds per pound. You can see where the confusion arose because someone then crossed out the pounds in the numerator of the fraction and the pounds in the denominator, leaving only seconds. Pounds force and pounds mass are not really the same thing though and this is why English units suck for engineering, and why specific impulse in seconds is so counterintuitive. But because early rocket engineers used English units, seconds of specific impulse has stuck as the industry standard.
Specific impulse reduces to units of seconds in both English and SI units. The measure is "specific" to the Earth's gravitation constant, regardless of whether the rocket is operating at sea level or in Space. It's the total impulse (in Newton-secs) per "weight" of propellant (in Newtons or kg*m/sec^2). So, we get Newton-sec per Newton which gives Isp the units of seconds.

It's an awkward meaningless unit, but it's the same value when comparing rocket engines/motors in both systems of measure:
Isp = Total impulse per weight of propellant.
Isp = Thrust per weight flow of propellant.​

For those who took Calculus and were looking for a reason to use it someday, here's the general equation:
(from Sutton).​

##### Well-Known Member
TRF Supporter
Isp reduces to the units of "sec", if one assumes that for example in English units that a pound-force (lbf) and a pound-mass (lbm) are equivalent. Rigorously, they are not the same, however, at sea level they are numerically equal. Hence, the convention has been taken that they are are the same and a lbf/lbm is assumed to be one and only the units of seconds remain.

#### ThirstyBarbarian

##### Well-Known Member
I learned a lot from this because I had just assumed “specific impulse” was a sudden and intense urge to act, but in a very narrowly defined and particular way.

#### OverTheTop

##### Well-Known Member
TRF Supporter
isp = amount of bounce to the ounce
I thought that was a measurement of kangaroo performance?

Anyway, as a BASIC description of Isp I tell people it is the rocketry equivalent of miles per gallon. That sort of gets the idea across quickly from my experience.

#### rocket_troy

##### Well-Known Member
TRF Supporter
It's an awkward meaningless unit, but it's the same value when comparing rocket engines/motors in both systems of measure:
Isp = Total impulse per weight of propellant.
Isp = Thrust per weight flow of propellant.​
I never found it awkward or meaningless - although I concede many do. It can always be reduced back to the amount of seconds a given amount of propellant can hover from the force it's capable of producing at sea level.

TP

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