Many of us have heard that phrase from NASA or other space enthusiasts, but what does it mean?
NOTE: I'll explain the rocket equation first. If you are familiar with it, you may want to skip down to the second part of the post- SSTOs.
The rocket equation, also known as the Tsiolkovsky Rocket Equation, was created by, you guessed it, Mr. Tsiolkovsky!
Remember, we're talking about Tsiolkovsky, this guy,
<Krazy Russian Rocket Scientist (Tsiolkovsky)
not Tchaikovsky.
<Krazy Russian Musician (Tchaikovsky)
(<3 you both)
Anywho, the rocket equation dictates what is possible with standard reaction mass rocket engines. Here it is:
where:
is delta-v – the maximum change of velocity of the vehicle (with no external forces acting).
is the initial total mass, including propellant, also known as wet mass.
is the final total mass without propellant, also known as dry mass.
is the effective exhaust velocity. Also,
---->where
is the specific impulse expressed as a time period
---->
is standard gravity = 9.80665 m/s2.
is the natural logarithm function.
(Courtesy of Wikipedia. Read more here: https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation)
All rocketry is done by changing the velocity of your rocket. What this equation says is that the amount you can change velocity is related to the efficiency of the engine you are using and the amount of mass that is passed through the engine (the change in mass). When you have many empty fuel tanks, those are added mass that you don't need. It's better to drop that mass off (stage) and this is the equation which says that staging is good. Infact, staging is better than good.
TYRANNY.
Staging isn't just good; it's necessary.
The rocket equation is referred to as "tyrannical" because it limits how big we can make spacecraft and what we can do with them.
If you keep adding fuel, you get more delta-v, but it gets to a point where your thrust/weight ratio decreases faster than the delta-v increases. To lift off the planet requires a thrust/weight ratio of 1.0 at very least (1.5-1.2 is best), and that limits the amount of mass you can lift.
This shows the deltav available by using a grasshopper engine and lifting only a probe core.
As you can see, at some point the delta-v gained seems to level off, and at that point, you would be adding more mass but negligible delta-v. Thus, we avoid operating in that region*. We prefer to make stages which operate in the steaper region of the chart and discard the stages when they are empty. If you would like to read more about how big to make stages, take a look at this discussion: https://jmnet.one/sfs/forum/index.php?threads/spacecraft-design-optimization.2282/ Since that topic is already covered, I'll discuss something else.
*SSTO.
Ok, here's the interesting stuff. (PART 2) --------------
SSTO means Single Stage To Orbit, but I will also refer to SSTLARs, Single Stage To Landing And Return.
These are spacecraft which do not stage at all, but all hardware which leaves the launch pad is able to return to earth. The only change in mass is the consumed fuel.
Since these spacecraft do not have the luxury of staging, they are entirely confined to the above chart, with one major note: a ship can have multiple engines, and if different types of engines are used, the isp and thus the delta-v will be different. Rather than only using the most efficient engine, it may be better to use a higher thrust (yet lower Isp) engine, which conserves volume and mass which can be put toward fuel.
Ok, which of the ships below has a higher delta-v or thrust/weight ratio?
Actually, both ships have identical thrust/weight ratios and delta-v. Think of it this way: the proportion of fuel mass to engine mass is the same in both. If you took an engine off the larger ship, it would have higher delta-v, but it would not have the twr to take off from earth.
Now add a probe control on the top of each.
Since that additional mass is constant, it makes up a smaller proportion in the larger ship. Thus, the larger ship would have more delta-v and a higher twr.
Let's say we wanted to use only Frontier engines to do a SSTO mission. It has to take off, so we decide to keep the twr of 1.17 which the ship has without a probe. Placing a probe core on it hurts that delta-v and twr, so we keep adding fuel and engines (one engine per huge fuel tank) until the probe core is an insignificant mass compared to the rest of the ship. At that point, we are basically at the same delta-v and twr that a single fuel tank and engine have without the control- the difference is, now we can control the ship. So as we add more fuel and engines (at a given proportion), we approach the ideal of that proportion. We can never exceed it.
Assuming this ship has the same twr, it has the same delta-v as a single fuel tank and a single engine would. The difference is, this ship takes the entire building area to make (0 free volume) but has control. Using some larger engines may allow for takeoff (constant twr) with less mass in engines. In orbit, we could just use the efficient engines. This would not add delta-v, though, but it would change the efficiency of the lunch. Now, we assumed this has the same twr as a single fuel tank and engine. If the twr is less than that (<1.17) it will waste too much energy at takeoff. If it is greater, than it might be wasteing mass on engines. I do not know what the ideal twr is for takeoff, nor have I learned how to calculate it (yet!).
So here's what we know:
The most efficient engine (other than the ion engine) is this Frontier engine we are using. Any craft which can lift off from earth will have a minimal twr of (let's say) 1.1. A smaller twr will just cause a less efficient takeoff, but a higher twr will reduce available delta-v, while increasing the efficiency of launch (to a point).
Other than the efficiency during launch, the below spacecraft has the best delta-v for a SSTO spacecraft. A spacecraft could have higher launch efficiency, but lower available delta-v. We will only consider the available (theoretical) delta-v, not the launch efficiency.
And remember, we can't control this craft, but if we scale it up and add a control probe, the specs of the new spacecraft will be effectively the same as this one.
So how much delta-v does this spacecraft have?
285*9.81*LN(98/(98-90*.9))= 4897.64 m/s.
Remember the giant spacecraft I showed? Even with different twrs, the delta-v wasted during launch means that no Frontier-using SSTO can ever exceed this amount.
Keeping the twr of 1.17, the Titan has a delta-v of 4804.75 m/s. The Broadsword has 4978.85 (Better!). The Hawk has 4902.60, and the Grasshopper has 4732.61 m/s. What about the ion engine? It cannot sustain that twr, as a single engine plus a solar panel for power has a twr less than 1 (0.94).
Thus, Broadswords might be the best engine to use for a SSTO, but no SSTO can ever achieve more than 5k delta-v. Even if the calculated delta-v is greater than 5k, it will waste too much to get into orbit, and thus cannot do a mission that requires 5k delta-v.
Now, other stages which are not required to lift off from the ground can have higher delta-v than this. A large fuel tank with a single engine can have huge amounts of delta-v, but they cannot lift off, so they cannot be a SSTO.
Recently I showed how a spaceship with three parts could be a SSTLAR, landing and safely flying back to earth for recovery, but that cannot be done for a mission that requires more than 5k delta-v. Now, a SSTO could use a mix of engines, using high thrust engines to reach orbit more efficiently, and then using high-efficiency engines for orbital maneuvers, but this will never reach substantially higher than 5k m/s of delta-v.
A mission to land on Mercury and return would take about 8k m/s of delta-v, so it is impossible for a SSTLAR to perform its mission on Mercury with the current technology. No amount of brilliant engineering or careful calculations will change that. Without engines that have both high ISP and high thrust, such a mission cannot be done.
That is why the rocket equation is referred to as a tyrant. It cannot be worked around.
NOTE: I'll explain the rocket equation first. If you are familiar with it, you may want to skip down to the second part of the post- SSTOs.
The rocket equation, also known as the Tsiolkovsky Rocket Equation, was created by, you guessed it, Mr. Tsiolkovsky!
Remember, we're talking about Tsiolkovsky, this guy,
not Tchaikovsky.
(<3 you both)
Anywho, the rocket equation dictates what is possible with standard reaction mass rocket engines. Here it is:
where:
---->where
---->
(Courtesy of Wikipedia. Read more here: https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation)
All rocketry is done by changing the velocity of your rocket. What this equation says is that the amount you can change velocity is related to the efficiency of the engine you are using and the amount of mass that is passed through the engine (the change in mass). When you have many empty fuel tanks, those are added mass that you don't need. It's better to drop that mass off (stage) and this is the equation which says that staging is good. Infact, staging is better than good.
TYRANNY.
Staging isn't just good; it's necessary.
The rocket equation is referred to as "tyrannical" because it limits how big we can make spacecraft and what we can do with them.
If you keep adding fuel, you get more delta-v, but it gets to a point where your thrust/weight ratio decreases faster than the delta-v increases. To lift off the planet requires a thrust/weight ratio of 1.0 at very least (1.5-1.2 is best), and that limits the amount of mass you can lift.
This shows the deltav available by using a grasshopper engine and lifting only a probe core.
As you can see, at some point the delta-v gained seems to level off, and at that point, you would be adding more mass but negligible delta-v. Thus, we avoid operating in that region*. We prefer to make stages which operate in the steaper region of the chart and discard the stages when they are empty. If you would like to read more about how big to make stages, take a look at this discussion: https://jmnet.one/sfs/forum/index.php?threads/spacecraft-design-optimization.2282/ Since that topic is already covered, I'll discuss something else.
*SSTO.
Ok, here's the interesting stuff. (PART 2) --------------
SSTO means Single Stage To Orbit, but I will also refer to SSTLARs, Single Stage To Landing And Return.
These are spacecraft which do not stage at all, but all hardware which leaves the launch pad is able to return to earth. The only change in mass is the consumed fuel.
Since these spacecraft do not have the luxury of staging, they are entirely confined to the above chart, with one major note: a ship can have multiple engines, and if different types of engines are used, the isp and thus the delta-v will be different. Rather than only using the most efficient engine, it may be better to use a higher thrust (yet lower Isp) engine, which conserves volume and mass which can be put toward fuel.
Ok, which of the ships below has a higher delta-v or thrust/weight ratio?
Actually, both ships have identical thrust/weight ratios and delta-v. Think of it this way: the proportion of fuel mass to engine mass is the same in both. If you took an engine off the larger ship, it would have higher delta-v, but it would not have the twr to take off from earth.
Now add a probe control on the top of each.
Since that additional mass is constant, it makes up a smaller proportion in the larger ship. Thus, the larger ship would have more delta-v and a higher twr.
Let's say we wanted to use only Frontier engines to do a SSTO mission. It has to take off, so we decide to keep the twr of 1.17 which the ship has without a probe. Placing a probe core on it hurts that delta-v and twr, so we keep adding fuel and engines (one engine per huge fuel tank) until the probe core is an insignificant mass compared to the rest of the ship. At that point, we are basically at the same delta-v and twr that a single fuel tank and engine have without the control- the difference is, now we can control the ship. So as we add more fuel and engines (at a given proportion), we approach the ideal of that proportion. We can never exceed it.
Assuming this ship has the same twr, it has the same delta-v as a single fuel tank and a single engine would. The difference is, this ship takes the entire building area to make (0 free volume) but has control. Using some larger engines may allow for takeoff (constant twr) with less mass in engines. In orbit, we could just use the efficient engines. This would not add delta-v, though, but it would change the efficiency of the lunch. Now, we assumed this has the same twr as a single fuel tank and engine. If the twr is less than that (<1.17) it will waste too much energy at takeoff. If it is greater, than it might be wasteing mass on engines. I do not know what the ideal twr is for takeoff, nor have I learned how to calculate it (yet!).
So here's what we know:
The most efficient engine (other than the ion engine) is this Frontier engine we are using. Any craft which can lift off from earth will have a minimal twr of (let's say) 1.1. A smaller twr will just cause a less efficient takeoff, but a higher twr will reduce available delta-v, while increasing the efficiency of launch (to a point).
Other than the efficiency during launch, the below spacecraft has the best delta-v for a SSTO spacecraft. A spacecraft could have higher launch efficiency, but lower available delta-v. We will only consider the available (theoretical) delta-v, not the launch efficiency.
And remember, we can't control this craft, but if we scale it up and add a control probe, the specs of the new spacecraft will be effectively the same as this one.
So how much delta-v does this spacecraft have?
285*9.81*LN(98/(98-90*.9))= 4897.64 m/s.
Remember the giant spacecraft I showed? Even with different twrs, the delta-v wasted during launch means that no Frontier-using SSTO can ever exceed this amount.
Keeping the twr of 1.17, the Titan has a delta-v of 4804.75 m/s. The Broadsword has 4978.85 (Better!). The Hawk has 4902.60, and the Grasshopper has 4732.61 m/s. What about the ion engine? It cannot sustain that twr, as a single engine plus a solar panel for power has a twr less than 1 (0.94).
Thus, Broadswords might be the best engine to use for a SSTO, but no SSTO can ever achieve more than 5k delta-v. Even if the calculated delta-v is greater than 5k, it will waste too much to get into orbit, and thus cannot do a mission that requires 5k delta-v.
Now, other stages which are not required to lift off from the ground can have higher delta-v than this. A large fuel tank with a single engine can have huge amounts of delta-v, but they cannot lift off, so they cannot be a SSTO.
Recently I showed how a spaceship with three parts could be a SSTLAR, landing and safely flying back to earth for recovery, but that cannot be done for a mission that requires more than 5k delta-v. Now, a SSTO could use a mix of engines, using high thrust engines to reach orbit more efficiently, and then using high-efficiency engines for orbital maneuvers, but this will never reach substantially higher than 5k m/s of delta-v.
A mission to land on Mercury and return would take about 8k m/s of delta-v, so it is impossible for a SSTLAR to perform its mission on Mercury with the current technology. No amount of brilliant engineering or careful calculations will change that. Without engines that have both high ISP and high thrust, such a mission cannot be done.
That is why the rocket equation is referred to as a tyrant. It cannot be worked around.
