I've made a previous post about Specific Impulse, but I've wanted to improve it for a while, since it's not very clear. This post is using a new system called MathJax to display equations, which should make them easier to read.
Specific impulse is essentially a measure of how efficiently a rocket engine converts the chemical potential energy of its fuel into the kinetic energy driving the rocket forward. It is defined as the thrust of a rocket engine $T$ divided by the weight flow rate $\dot{W}$: $$I_{sp}=\frac{T}{\dot{W}}$$ First, we need to distinguish between weight and mass. Mass is how much matter an object consists of, while weight is the force exerted on an object by the local gravitational field. The local gravity on Earth exerts 9.81 m/s^2 of acceleration on everything, so if force = mass times acceleration, the force, or weight, exerted by an object with 1 kg of mass is 1 kg * 9.81 m/s^2. Since one Newton is the amount of force needed to accelerate one kg at 1 m/s^2, the object has a weight of 9.81 N. Weight is normally measured in kilograms (or pounds, but they're the same dimensionally), which seems odd, since we know weight can change independently of mass on different planets with different gravities. This is because the unit commonly referred to by a kilogram is actually kilogram-force, or a kilopond, which is exactly the force of one kilogram of mass in standard Earth gravity, or about 9.81 N. Therefore, in common use, both the definition and unit of mass and weight are the same.
Specific impulse $I_{sp}$ is defined as the thrust $T$ produced by a rocket engine, divided by the weight flow rate of propellant $\dot{W}$, or: $${I_{sp}}=\frac{T}{\dot{W}}$$ It seems like it should be thrust per unit weight of propellant consumed, but thrust is instantaneous, so it wouldn't make sense without converting to some weird unit like newton-seconds.
Since $\dot{W}$ is weight, and weight is mass multiplied by standard gravity, the weight flow rate is the mass flow rate $\dot{m}$ multiplied by gravity: $$\dot{W}=g\dot{m}$$ The mass flow rate is the first derivative of the propellant mass $m_p$ with respect to time: $$\dot{m}=\frac{dm_p}{dt}$$ Therefore: $$\dot{W}=g\frac{dm_p}{dt}$$
Thrust is simply the exhaust velocity of the propellant from the engine $v_e$ multiplied by the mass flow rate $\dot{m}$ which is exactly the same as the mass flow rate already defined: $$T=v_e\frac{dm_p}{dt}$$
If we substitute these back into the original $I_{sp}$ formula, we get: $$I_{sp}=\frac{v_e\frac{dm_p}{dt}}{g\frac{dm_p}{dt}}$$ Since the mass flow rate is on both the top and bottom of the equation, we can get rid of them, and get: $$I_{sp}=\frac{v_e}{g}$$ The important thing to remember here is that $g$ is a constant in this equation. It is quite literally the acceleration due to gravity at the earth's surface, regardless of where the rocket engine is, or what kind of gravity it is in. In fact, any constant with the unit of $m/s^2$ would work. Not only that, but when calculating $\Delta{V}$ using a specific impulse term, as is frequently seen, the specific impulse term is multiplied by $g$, turning the term back into $v_e$. Another weird effect of this is that specific impulse has a unit of seconds.
This weird definition was originally used, as far as I can tell, because the unit of seconds is the same whether you're using metric or imperial units to calculate it, which is less confusing than m/s and ft/s. Using metric units, exhaust velocity and specific impulse can be calculated approximately by multiplying or dividing by ten. In short, specific impulse is a way of making exhaust velocity, which is the real measure of rocket engine efficiency, into a number which is the same whatever units you use to calculate it.
Interestingly, $v_e$ is effective exhaust velocity, which takes into account any propellant not exhausted at the full velocity of the engine, such as with turbine exhaust or film cooling. Effective exhaust velocity can be calculated on an existing engine with the specific impulse formula by using: $$v_e=\frac{T}{\dot{m}}$$ Except $T$ and $\dot{m}$ are based on measurements of a engine rather than calculated.
Monday, May 21, 2018
Thursday, December 28, 2017
History of the Delta rocket Pt. 2: Delta-B to Delta-N
Last time we stopped our review at the first of the Delta rockets proper, the Delta-A. The Delta-B was the next variant of the Delta family, and was very similar, with a lengthened second stage and an upgraded second stage engine, the AJ-10-118D. The Delta-A used the AJ-10-118.
The AJ-10-118D burns unsymmetrical dimethylhydrazine (UDMH) as a fuel, and inhibited red fuming nitric acid (IRFNA) as an oxidizer, instead of UDMH and white fuming nitric acid (WFNA), which is what the AJ-10-118 used. Variants of the AJ-10 have been used on the Apollo program, the Space Shuttle program, and are planned to be used on the Orion program.
Fuming nitric acid is more concentrated than concentrated nitric acid (>86% vs ~68%), and WFNA is nearly pure nitric acid. It makes lab gloves burst into flames.
WFNA and IRFNA are both hypergolic with UDMH. IRFNA has slightly higher performance than WFNA, however it is also considerably more dangerous, as in addition to being corrosive to almost everything, it is also more toxic and gives off nitrogen dioxide fumes. IRFNA has an inhibitor added to prevent it from being quite as corrosive. If you want to read more about this kind of thing, I can't recommend Ignition! highly enough.
Delta-B launched nine times, with one failure. The Delta-C increased the fairing size, and used an upgraded 3rd stage. It launched 13 times, with one failure.
The Delta-D, aka the Thrust Augmented Delta, added 3 strap-on Castor I solid boosters to the first stage. The Delta-E was known as the Thrust Augmented Improved Delta, with Castor 2 solid boosters, and increased the thrust of the first stage engine, the MB-3 (in this case, MB-3-III), which is part of the LR-79 family. Some sources say that the upgrade to the MB-3-III was on the Delta-D, but most say Delta-E. The second stage was made restartable, and was enlarged, along with the fairing. The third stage was changed again, and another third stage was available as an option, with which it was known as the Delta-E1.
Delta-F would have been similar to the Delta-E, but without the solid boosters, but was never built. Delta-G was a one-off, built for just two launches, Biosatellite 1 and 2, and lacking the third stage. Delta-H was similar to the Delta-G, but without the solid boosters, but was never built. Delta-I was never built, likely to avoid confusion with a possible future Delta One. Delta-J had yet another third stage, and launched just once. Delta-K was a design for a Delta with a liquid oxygen/liquid hydrogen upper stage, and was never built.
Delta-L introduced the Extended Long Tank first stage, which was longer, and not tapered. Delta-M and -N were very similar, but with different third stages. There were variants of the Delta-M and -N, known as Delta-M6 and -N6, which had six, rather than three solid boosters.
In 1972, Delta numbering systems changed from the old letter system to a four-digit numbering system. Next time, I'll cover everything under that system.
The AJ-10-118D burns unsymmetrical dimethylhydrazine (UDMH) as a fuel, and inhibited red fuming nitric acid (IRFNA) as an oxidizer, instead of UDMH and white fuming nitric acid (WFNA), which is what the AJ-10-118 used. Variants of the AJ-10 have been used on the Apollo program, the Space Shuttle program, and are planned to be used on the Orion program.
Fuming nitric acid is more concentrated than concentrated nitric acid (>86% vs ~68%), and WFNA is nearly pure nitric acid. It makes lab gloves burst into flames.
WFNA and IRFNA are both hypergolic with UDMH. IRFNA has slightly higher performance than WFNA, however it is also considerably more dangerous, as in addition to being corrosive to almost everything, it is also more toxic and gives off nitrogen dioxide fumes. IRFNA has an inhibitor added to prevent it from being quite as corrosive. If you want to read more about this kind of thing, I can't recommend Ignition! highly enough.
Delta-B launched nine times, with one failure. The Delta-C increased the fairing size, and used an upgraded 3rd stage. It launched 13 times, with one failure.
The Delta-D, aka the Thrust Augmented Delta, added 3 strap-on Castor I solid boosters to the first stage. The Delta-E was known as the Thrust Augmented Improved Delta, with Castor 2 solid boosters, and increased the thrust of the first stage engine, the MB-3 (in this case, MB-3-III), which is part of the LR-79 family. Some sources say that the upgrade to the MB-3-III was on the Delta-D, but most say Delta-E. The second stage was made restartable, and was enlarged, along with the fairing. The third stage was changed again, and another third stage was available as an option, with which it was known as the Delta-E1.
Delta-F would have been similar to the Delta-E, but without the solid boosters, but was never built. Delta-G was a one-off, built for just two launches, Biosatellite 1 and 2, and lacking the third stage. Delta-H was similar to the Delta-G, but without the solid boosters, but was never built. Delta-I was never built, likely to avoid confusion with a possible future Delta One. Delta-J had yet another third stage, and launched just once. Delta-K was a design for a Delta with a liquid oxygen/liquid hydrogen upper stage, and was never built.
Delta-L introduced the Extended Long Tank first stage, which was longer, and not tapered. Delta-M and -N were very similar, but with different third stages. There were variants of the Delta-M and -N, known as Delta-M6 and -N6, which had six, rather than three solid boosters.
In 1972, Delta numbering systems changed from the old letter system to a four-digit numbering system. Next time, I'll cover everything under that system.
Wednesday, November 29, 2017
History of Delta rocket Pt. 1
I waited too long too start writing this post, so I'm going to divide it into multiple parts.
The history of the Delta rocket begins with the PGM-17 Thor, which was an intermediate range ballistic missile (IRBM) with a range of 2,400km. It was designed to be able to hit Moscow from a launch site in the UK, and first flew in 25 January 1957, seven months after Douglas Aircraft was contracted to build it.
The missile used an LR-79 engine for its first (and only) stage, along with two LR-101 Vernier engines, for roll control. Its propellants were LOX and RP-1.
However, the missile was modified many times between this and the Delta, including changing the engine, and I won't go over them all.
The engine of missile 101 failed immediately after lifting off the pad, and the rocket fell back to the pad and exploded. It was determined that the failure was due to debris in the engine, from a LOX filling line that crews dragged over a patch of sand.
Missile 102 was erroneously destroyed by range safety (footage later in the above video), missile 103 exploded four minutes before the planned launch, and 104 broke up due to an electronics failure.
105 finally succeeded, but the Thor missile remained unreliable for many flights, mostly due to its turbopump design, which was eventually fixed.
The only other notable event in the Thor's history was the launch Bluegill Prime, on July 26th 1962, as part of Operation Fishbowl, which was a series of upper atmosphere nuclear weapons tests.
The history of the Delta rocket begins with the PGM-17 Thor, which was an intermediate range ballistic missile (IRBM) with a range of 2,400km. It was designed to be able to hit Moscow from a launch site in the UK, and first flew in 25 January 1957, seven months after Douglas Aircraft was contracted to build it.
The missile used an LR-79 engine for its first (and only) stage, along with two LR-101 Vernier engines, for roll control. Its propellants were LOX and RP-1.
However, the missile was modified many times between this and the Delta, including changing the engine, and I won't go over them all.
The engine of missile 101 failed immediately after lifting off the pad, and the rocket fell back to the pad and exploded. It was determined that the failure was due to debris in the engine, from a LOX filling line that crews dragged over a patch of sand.
Missile 102 was erroneously destroyed by range safety (footage later in the above video), missile 103 exploded four minutes before the planned launch, and 104 broke up due to an electronics failure.
105 finally succeeded, but the Thor missile remained unreliable for many flights, mostly due to its turbopump design, which was eventually fixed.
The only other notable event in the Thor's history was the launch Bluegill Prime, on July 26th 1962, as part of Operation Fishbowl, which was a series of upper atmosphere nuclear weapons tests.
The rocket exploded on the pad, destroying the nuclear warhead and contaminating the pad with plutonium.
Thor was modified with several upper stages for use as a orbital launch vehicle. This first was Thor-Able (Able is the name of the upper stage, but was named Able because it is the first modification of Thor, and the first in the allied military phonetic alphabet).
The next variant was not Thor-Bravo, but Thor-Agena. Agena was an already existing upper stage/satellite bus, with stabilization, communications, and power built in. When those were removed, it was known as an Ascent Agena. It used Bell 8048, 8081, and 8096 engines burning JP-4 and IRFNA, on Agena -A, -B, and -C respectively. Attitude control was provided by nitrogen-freon cold gas thrusters.
Then the Thor-Ablestar was designed, which was the same as Thor-Able, but with a larger Able upper stage.
After this, the Thor-Delta was built. This is the first Delta rocket, which will be henceforth referred to as the Delta-A. The first stage used a Rocketdyne MB-3 engine, and the second stage (derived from the able upper stage) used an AJ-10-118 engine burning hydrazine and nitric acid. It first flew on May 13 1960, with a solid third stage. The first flight was a failure, but the second flight, in August, successfully launched NASA's first communications satellite, Echo 1A, ("A" due to the previous launch being a failure) into orbit.
Monday, October 30, 2017
ITS/BFR design updates
At the last IAC, Elon Musk presented the latest changes to the BFR.
Throughout this post, I will be referring to what was previously the ITS as the BFR, as that appears to be what SpaceX now refers to it as externally now. The interplanetary spaceship will be refered to as the BFS, and the booster will be called the BFB.
Some of the numbers were changed between the presentation and the PDF being posted. One of these changes was a factual error, about the internal cabin volume of the BFS, and the other was a change of the total BFB thrust, and the removal of the total BFR mass. For this post, I will mostly use the numbers from the presentation, as they are more complete, but I will note where the numbers differ or are wrong.
Overall:
The reusable payload to LEO has been cut by about half, from 300t to 150t. The payload to Mars has gone from 450t to 150t, and the goal for the number of people per flight has gone from 100+ to 100.
Raptor
The Raptor engine is further along in development than last time, and has been slightly downscaled to match the smaller BFR. This is because it is harder to make engines throttle to lower percentages of full thrust, which they would need to do to land safely, and still have redundancy.
"The engine thrust dropped roughly in proportion to the vehicle mass reduction from the first IAC talk" (source)
Elon Musk said in the presentation that the Isp had the potential to be increased by 5-10 seconds, and the chamber pressure by 50 bar, which would make the 2017 Raptor have the same stats as the 2016 one.
(2017)(2016)
250bar vs 300bar
Deep throttle to 20%/ 20%
Vac
Exit diameter 2.4m/ expansion ratio 200
thrust 1,900kn/ 3,500kn
isp 375s/ 382s
SL
exit dia 1.3m/ expansion ratio 40
Thrust (SL) 1,700kn/ (SL) 3,050kn
Isp (SL) 330s, (Vac) 356s/ Isp (SL) 334s, (Vac) ???
BFB
Dimensions:
(2017)(2016)
58m x 9m/ 77.5m x 12m
Mass is tricky, as the video of the presentation gives exact values, while the PDF of the slides give a different exact value for thrust, and no numbers for mass. For this post, I'll use the numbers described in the presentation. Dry and prop masses are based on ratios from the 2016 BFB.
Mass (dry, prop, wet, prop mass fraction[prop/wet])
275t, 6700t, 6975t, ~0.96
to
~126.75t, ~3,088.25t, 3215t, ~0.96
Engines:
(2017)(2016)
31/ 42
(Apparently the important scientific and fictional reasons weren't that important, however the PDF does not say how many engines it has, which means that it is likely changing.)
Thrust:
This is weird. The talk showed a thrust of 5400 tons, which is equal to 48040.79kn, which is how much thrust 28 and a quarter SL raptors produce ASL. It's possible that this is a mistake, as there was also a mistake in the interior volume of the BFS, but it's also possible that it was from a different version of raptor.
In the PDF, this was changed to 52,700kn, which is exactly what 31 SL raptors produce ASL, lending weight to the theory that this was a typo. I'm going to assume that it was a typo.
(2017)(2016)
52,700kn/ 128mn (SL) 138mn (Vac)
Delta-V
Vac:
11288.2m/s / ???
SL:
10463.8m/s / 10590.47m/s
(note: this seems odd, as the thrust and fuel mass are roughly double in the 2016 BFR, but remember that Delta-V is a function of propellant ratio and Isp, and I assume the propellant ratio to be the same. Basically, scaling up or down a spaceship design just changes how much extra payload affects Delta-V)
BFS:
The spaceship's largest change, aside from size, is in shape. The 2016 IAC spaceship had a much more complex body shape, with 3 fins that blended into the overall shape of the ship. The 2017 ship is much simpler, with a simple cylindrical shape and a single set of delta wings. This was done to avoid building a "box in a box" (source)
The BFS now refuels via a connection at the end of the ship, rather than at the side.
Size
(2017)(2016)
48m x 9m/ 49.5m x 17m (max) 12m (base)
Mass
Using the masses from the interplanetary ship in the 2016 numbers.
(2017)(2016)(dry, prop, wet, prop mass fraction[prop/wet])
85t, 1,100t, 1,185, ~.93 / 150t, 1,950t, 2100t, ~0.93
(In the presentation, Elon Musk said that the current design has the dry mass as 75t, but mass growth would likely occur)
Delta-V
(All vac)
9689.63m/s / 9886.28 m/s
Engines
4 Vac, 2 SL/ 6 Vac, 3 SL
Thrust
Vac
7,600kn/ 21,000kn
SL
3,400kn/ 9,150kn
However, Elon Musk said here that a 3rd medium area Raptor was added to the BFS since the IAC. I don't know what form this would take, or how this would fit on the BFS.
Throughout this post, I will be referring to what was previously the ITS as the BFR, as that appears to be what SpaceX now refers to it as externally now. The interplanetary spaceship will be refered to as the BFS, and the booster will be called the BFB.
Some of the numbers were changed between the presentation and the PDF being posted. One of these changes was a factual error, about the internal cabin volume of the BFS, and the other was a change of the total BFB thrust, and the removal of the total BFR mass. For this post, I will mostly use the numbers from the presentation, as they are more complete, but I will note where the numbers differ or are wrong.
Overall:
The reusable payload to LEO has been cut by about half, from 300t to 150t. The payload to Mars has gone from 450t to 150t, and the goal for the number of people per flight has gone from 100+ to 100.
Raptor
The Raptor engine is further along in development than last time, and has been slightly downscaled to match the smaller BFR. This is because it is harder to make engines throttle to lower percentages of full thrust, which they would need to do to land safely, and still have redundancy.
"The engine thrust dropped roughly in proportion to the vehicle mass reduction from the first IAC talk" (source)
Elon Musk said in the presentation that the Isp had the potential to be increased by 5-10 seconds, and the chamber pressure by 50 bar, which would make the 2017 Raptor have the same stats as the 2016 one.
(2017)(2016)
250bar vs 300bar
Deep throttle to 20%/ 20%
Vac
Exit diameter 2.4m/ expansion ratio 200
thrust 1,900kn/ 3,500kn
isp 375s/ 382s
SL
exit dia 1.3m/ expansion ratio 40
Thrust (SL) 1,700kn/ (SL) 3,050kn
Isp (SL) 330s, (Vac) 356s/ Isp (SL) 334s, (Vac) ???
BFB
Dimensions:
(2017)(2016)
58m x 9m/ 77.5m x 12m
Mass is tricky, as the video of the presentation gives exact values, while the PDF of the slides give a different exact value for thrust, and no numbers for mass. For this post, I'll use the numbers described in the presentation. Dry and prop masses are based on ratios from the 2016 BFB.
Mass (dry, prop, wet, prop mass fraction[prop/wet])
275t, 6700t, 6975t, ~0.96
to
~126.75t, ~3,088.25t, 3215t, ~0.96
Engines:
(2017)(2016)
31/ 42
(Apparently the important scientific and fictional reasons weren't that important, however the PDF does not say how many engines it has, which means that it is likely changing.)
Thrust:
This is weird. The talk showed a thrust of 5400 tons, which is equal to 48040.79kn, which is how much thrust 28 and a quarter SL raptors produce ASL. It's possible that this is a mistake, as there was also a mistake in the interior volume of the BFS, but it's also possible that it was from a different version of raptor.
In the PDF, this was changed to 52,700kn, which is exactly what 31 SL raptors produce ASL, lending weight to the theory that this was a typo. I'm going to assume that it was a typo.
(2017)(2016)
52,700kn/ 128mn (SL) 138mn (Vac)
Delta-V
Vac:
11288.2m/s / ???
SL:
10463.8m/s / 10590.47m/s
(note: this seems odd, as the thrust and fuel mass are roughly double in the 2016 BFR, but remember that Delta-V is a function of propellant ratio and Isp, and I assume the propellant ratio to be the same. Basically, scaling up or down a spaceship design just changes how much extra payload affects Delta-V)
BFS:
The spaceship's largest change, aside from size, is in shape. The 2016 IAC spaceship had a much more complex body shape, with 3 fins that blended into the overall shape of the ship. The 2017 ship is much simpler, with a simple cylindrical shape and a single set of delta wings. This was done to avoid building a "box in a box" (source)
The BFS now refuels via a connection at the end of the ship, rather than at the side.
Size
(2017)(2016)
48m x 9m/ 49.5m x 17m (max) 12m (base)
Mass
Using the masses from the interplanetary ship in the 2016 numbers.
(2017)(2016)(dry, prop, wet, prop mass fraction[prop/wet])
85t, 1,100t, 1,185, ~.93 / 150t, 1,950t, 2100t, ~0.93
(In the presentation, Elon Musk said that the current design has the dry mass as 75t, but mass growth would likely occur)
Delta-V
(All vac)
9689.63m/s / 9886.28 m/s
Engines
4 Vac, 2 SL/ 6 Vac, 3 SL
Thrust
Vac
7,600kn/ 21,000kn
SL
3,400kn/ 9,150kn
However, Elon Musk said here that a 3rd medium area Raptor was added to the BFS since the IAC. I don't know what form this would take, or how this would fit on the BFS.
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