ISP for idiots

[Kaito]

I've been attempting to wrap my mind around the whole idea of Specific Impulse. For some reason, I cannot seem to get it. Why is it measured in seconds? What does it mean? And, according to this article, a turbofan has MUCH more impulse then the SSME's. So, why dont we just take up a turbofan along with oxygen, and use them? It will be much more fuel efficient, unless my understand is messed up.

So, can someone explain this to me?

 

[Artlav]

Get on something with good wheels on a flat surface and take a load of heavy bags.
Throw one bag back - you will move forward some distance.
Throw the second bag with same force - you will move a bit more.
...
Throw the last bag - you will move much more.

Each push from matter exhausted pushes all the matter that is left, the higher the velocity or higher the mass, the more push there will be. Mass by velocity is impulse, as defined in mechanics.

Each kilogram of mass exhausted provide a defined amount of impulse, the higher the value, the more efficient the engine. That value - mass*(mass*velocity)/time is the ISP. Why is it in seconds is a story on unit systems and history.

Now, a jet turbofan only carry fuel, not reaction mass, which is air in that case, so it's not strictly comparable to rocket engines.
The ISP of it will be fuel ISP, while for a rocket it's reaction mass ISP.

 

[SiberianTiger]

I've been attempting to wrap my mind around the whole idea of Specific Impulse. For some reason, I cannot seem to get it. Why is it measured in seconds? What does it mean? And, according to this article, a turbofan has MUCH more impulse then the SSME's. So, why dont we just take up a turbofan along with oxygen, and use them? It will be much more fuel efficient, unless my understand is messed up.

So, can someone explain this to me?

Why seconds? Simple.

Isp = F * DeltaT / (DeltaM * g)

which is

Isp = kg*m/s^2 * s / (kg*m/s^2) = s

which is a unit of time.

An ISP is calculated per the onboard store of a propellant (DeltaM is a change of mass of the spacecraft or aircraft during DeltaT). An air breathing engine "cheats" through using an outside air as a propellant (partly) and as a reaction mass. You would take a really huge amount of oxygen for it to work in space.

 

[T.Neo]

And, according to this article, a turbofan has MUCH more impulse then the SSME's. So, why dont we just take up a turbofan along with oxygen, and use them? It will be much more fuel efficient, unless my understand is messed up.

A turbofan achieves a much higher ISP by utilizing air as oxidizer, which is not available in space.

 

[Kozak]

Specific Impulse is just a measure of effectiveness of a drive. That is, if you take an AMRAAM and an SRB, they'll have quite the same ISP - just because they're built on similar technologies.

In numbers - it is just effective exhaust velocity, multiplied by coefficient of G.

As for turbofans:
Impulse, produced by engine, is proportional to reaction mass. But, if you reduce reaction mass n times, required energy to support the same impusle grows n^2 times. Same applies in reverse - if you reduce "throwed" mass n times, you reduce required energy en-square.

The only problem is your reaction mass reserve. Turbofans just "cheat" by getting it from the environment - that is, they spend 1kg of fuel to throw 9kgs of air. Consequently, they eject 10 times more mass - taking the same amount of energy produced by 1 kg of fuel, we get ~3.16 times mor impulse from one kg. Thus, taking aturbojet with an oxidizer wil just give you an ineffective rocket motor.

 

[Urwumpe]

Seconds is what you get, when bachelors of science do math.

Specific impulse is impulse/mass. or: The thrust force you get per unit of mass burned per unit of time.

In SI units, you will get the following units:
impulse => kg*m/s = N * s (as N = kg * m/s²)
mass => kg

So the resulting unit for specific impulse is N * s /(kg) = kg * (m/s) /kg.

This can be further reduced to m/s - it is equivalent to the average exhaust velocity.

In the US pseudo-imperial units, you will get:

impulse = lb(m) * ft/s
mass = lb(m)

specific impulse = impulse/mass = lb(m)/lb(m) * ft/s = ft/s

Now... where are the seconds?

If you use the alternative definition of impulse (p = dF/dt), your equation will look like that:

specific impulse = thrust force/mass flow

In SI units:
force : N (=kg m/s²)
mass flow: kg/s

and thus is measured in N/(kg/s) = N*s/kg (see above) or m/s.

In pseudo-imperial units:
force: lb(f).
mass flow: lb(m)/s

So it is measured in lb(f) * s/lb(m). Now, some people had been lazy and thought: lb is lb, it does not matter if it is force or mass!

So you get: lb* s/lb = s.

Physically wrong as force is not equal to mass (and only proportional to mass if you talk about inertia). But gives very simple short numbers and has a simple unit.

You can imagine this as such: If your rocket has an ISP of one second, this means that your rocket engine would be able to burn for one second, if it has to produce one lb of thrust force and has one lb of fuel mass for feeding it.

 

[agentgonzo]

In laymans terms, the specific impulse (as measured in seconds) would be the amount of time that a certain mass of fuel could hold up its own weight and hover at sea level (if you could run the engine in that way).

So 1kg of fuel for the SSMEs would be able to make a 1kg engine hover for 453s in ideal conditions (not counting the weight of the fuel itself).

 

[Linguofreak]

A turbofan achieves a much higher ISP by utilizing air as oxidizer, which is not available in space.

Actually, the fact that they use air as reaction mass is much more important as a determiner of ISP than the fact that they use it as oxidizer. The effect is still the same, though, no air means no oxidizer and no reaction mass for a jet engine, means no jet engines in space.

---------- Post added at 12:34 AM ---------- Previous post was at 12:32 AM ----------

So, why dont we just take up a turbofan along with oxygen, and use them? It will be much more fuel efficient, unless my understand is messed up.

Because a turbofan has a much, much lower ISP when it has to carry reaction mass with it as well as fuel and oxidizer.

 

[Pquardzvaark]

It should also be noted that turbofans don't have the thrust-to-weight of a rocket engine, so you'd have a hard time getting a vertical take-off LV using turbofans. So even though it can help early on during the flight, it's more of a burden since you'll need a horizontal take-off LV.

 

[kwan3217]

Meters per second is a much better idea of rocket effectiveness. It's just how fast you throw exhaust out the back. Much more intuitive than how long you can burn a pound of fuel to get a pound of thrust.

This is one of those conventions that just infuriates me, along with electrons having negative charge and the base unit kilogram having a multiplier in its name. Alas, some things will never change, and in 1000 years people will be asking the same questions.

If only I had a time machine...

 

[Andy44]

Seconds is a better unit to use when comparing rockets to air-breathing jets.

When speaking only of rockets m/s makes more sense. But we shouldn't call that specific imulse, it should be called effective exhaust velocity or something to reduce confusion.

 

[ar81]

ISP (specific impulse) is the period of time it takes for 1 unit of mass of mixture of fuel and oxidizer to produce 1 unit of force. Since it is a measure of time, units used are seconds.

Even if ISP is particular for each mixture, the exact value may vary based on operation conditions and design of the rocket. This is why different values may be assigned to the same mixture or a combination of mixtures.

ISP indicates the efficiency of the mixture. The higher the number, the more efficiency you get.

Impulse in the other side is the amount of "motion" of an object in a closed system, and it is somehow different than the ordinary concept of impulse common people use. The definition was set by Isaac Newton in his second law, and he called impulse as vi motrici, meaning some sort of "motion force".

Impulse = mass * velocity

It means that to obtain more impulse (a more powerful rocket), you may need to either throw mixture out of the exhaust faster (velocity), or you may need more mixture (mass).

Chemical reactions for certain mixtures and certain operation conditions (like temperature, for example) end up rpoviding a certain velocity of mixture coming out of the exhaust of the rocket. So, since velocity is fixed, you need more mixture to produce more impulse, and that's why a bigger fuel tank is required.

VASIMR rocket being designed by Adastra Rocket changes that, since velocity of the particles that are thrown out of the exhaust may vary, it means the same mass of mixture could produce more impulse. This is why VASIMR may revolutionize space travel.

 

[RisingFury]

The main reason why you cannot use a turbofan to get to space is that a turbofan only works in the atmosphere.

Yes, dragging along your fuel and oxidizer will allow you to keep the thing burning... but it's not the fuel combustion that is the main provider of thrust.

A turbofan has massive blades and can move huge amounts of air through the engine, while at the same time using only enough fuel, to keep the engine spinning

But, when you get higher and you lack your air... sure, you still have some exhaust force, but all the advantage of the blades - moving the other air through the engine - are gone.

 

[Tommy]

Actually, the fans on a Turbojet aren't for propulsion. The fans in the front compress the incoming air, and the fans in the back are for powering the front fans and electrical.

What makes the air flow through a jet engine is the difference in temperature between the air coming in and the air exiting. This is why jets and turbine engines perform better in the cold. Fuel is burned to create heat, and cause the heat difference. It's theoretically possible to use another heat source (plasma from a fusion reactor, or laser ,etc) to heat the air.

 

[Hielor]

Actually, the fans on a Turbojet aren't for propulsion. The fans in the front compress the incoming air, and the fans in the back are for powering the front fans and electrical.

What makes the air flow through a jet engine is the difference in temperature between the air coming in and the air exiting. This is why jets and turbine engines perform better in the cold. Fuel is burned to create heat, and cause the heat difference. It's theoretically possible to use another heat source (plasma from a fusion reactor, or laser ,etc) to heat the air.

The point still stands that the engines don't use the incoming air just for combustion, they also use it directly for propulsion. It would be completely infeasible to carry enough air to keep a jet engine running effectively in a vacuum.

 

[Andy44]

Actually, the fans on a Turbojet aren't for propulsion. The fans in the front compress the incoming air, and the fans in the back are for powering the front fans and electrical.

You are incorrect due to the terminology you are using.

An axial flow turbofan engine has three distinct sets of rotating blades, in order: the fans, the compressor, and the turbine.

The fans are indeed used to produce thrust, and most of the air that passes through them is blown out through ducts and bypasses the rest of the engine. Thus the term "high-bypass turbofan".

The compressor blades should not be referred to as "fans" because they are not fans, they compress the air.

And finally, the turbine blades are not a fan, either; you could call them "impellers", since they do not force gasses, but are rather forced by hot gasses exiting the combustion chamber. The turbine in turn turns the main shaft which turns the fan and compressor blades.

A simple turbojet engine has no fan blades and relies on hot turbine exhaust alone for thrust; this type of engine is rarely used anymore, since a turbofan's fan is responsible for most of its thrust and makes for a much more efficent engine.

 

[Tommy]

Sorry for the bad terminology, but the point is that turbine engines (including turbo-fans) don't rely on the expansion of the fuel as it combusts (the way a piston engine or some rocket engines do), but function because of the heat created by said combustion. With current tech, burning fuel is the only practical way to create enough heat to move enough air fast enough.

 

[agentgonzo]

Actually, the fans on a Turbojet aren't for propulsion. The fans in the front compress the incoming air, and the fans in the back are for powering the front fans and electrical.

They were talking about Turbofans. You are correct in what you say about the Turbojet, however.

And the power for a jet comes from both the heat (as you say) and the expansion of the fuel as it burns and becomes gaseous.

 

[Urwumpe]

Sorry for the bad terminology, but the point is that turbine engines (including turbo-fans) don't rely on the expansion of the fuel as it combusts (the way a piston engine or some rocket engines do), but function because of the heat created by said combustion. With current tech, burning fuel is the only practical way to create enough heat to move enough air fast enough.

Sorry, but this is wrong.

First of all, the fuel never combusts, but the fuel+oxidizer(air) mixture.

Next, this results always in an increase in volume - the exhaust wants to expand, as the temperature of the volume of exhaust increases. By the ideal gas law, this means, if the volume is constant, that the static pressure has to raise. For equalizing the pressure of the exhaust with the ambient air, the exhaust has to expand. The expansion results in a flow from high static pressure at the combustion cans, to lower static pressure at the beginning of the turbine. The pressure behind the turbine is even lower, so flow takes place through the turbine. This pressure drop is additionally amplified by the pressure drop of the turbine itself - the work which you extract from the hot exhaust, by slowing it down a bit. The next pressure drop takes place in the nozzle of the jet engine. usually, the exhaust is choked by the convergent part of the nozzle and accelerated to sonic speed, to be then further expanded and accelerated by the divergent part.

There is no practical difference in how the exhaust is used between a rocket engine and a jet engine. The only difference is the engine cycle: In rocket engines, you don't have the turbine behind the main combustion chamber, but instead drive it either by burning a small part of the propellants in gas generators, or use the heat of the main combustion chamber for vaporizing one propellant component (expander cycle) for producing the needed static pressure to drive a turbine. You may imagine a rocket engine as a turbojet, which produces over 99% of its thrust by the afterburner. (And in fact, a afterburner gets very close to the fuel consumption of a rocket engine)

Rocket engines can thus produce higher exhaust velocities (as there is no turbine behind the combustion chamber to slow the exhaust down), but at the price of complexity.

 

[agentgonzo]

First of all, the fuel never combusts, but the fuel+oxidizer(air) mixture.

Semantics...