* Copyright 2023 Robert Clark*

Given the Raptors repeated history of leaking fuel and catching fire I was surprised the booster was able to complete its portion of the ascent with no engine failures.

__Hypothesis__: the booster flew without engine failures because it throttled down to < 75%. The Starship had engine failures because it ran at ~90%, like the booster did on the first test flight with its multiple engine failures.

**Throttle Down Calculated by Propellant vs. Time Graph.**

Two separate observers, u/jobo555 and @space_josiah found fairly constant propellant flow rate, and therefore throttle, before where the booster begins to prepare for stage separation. Rocket thrust is given by (thrust) = (exhaust speed)*(propellant flow rate). So can get degree of throttle by propellant flow rate.

The graphs give the percentage of propellant remaining vs time. From this we can calculate the percentage change rate as the slope. For the booster it’s about 0.5%/s, 0.005/s as a decimal. Then given the total propellant load of 3,400 tons, in absolute term that propellant flow rate is 17 tons per second.

But the full thrust propellant flow rate for each Raptor v2 can be calculated as:

props flow rate = thrust/exhaust speed = 230,000*9.81/(327*9.81) = 700 kg/s. Then for all 33 engines on the booster that’s 33*700 kg/s = 23,100 kg/s, 23.1 tons/s. Then the throttle down for the booster amounted to: 17/23.1 = .736, less than 75%.

For the Starship, from the first image below, in its second graph we see from 4 minutes to 8 minutes, 240 seconds, the propellant level dropped from ~80% to ~5%, for a percentage rate drop of 75/240, 0.313%/s. Then the absolute flow rate for a 1,200 ton prop load is 3.756 tons per second. But for the 6 engines the flow rate at full thrust would be 6*700 = 4,200 kg/s, 4.2 tons/s. Then the throttle is .894, ~90%.

Note that throttling down to 75% also correspondingly drops the combustion chamber pressure from 300 bar to about 225 bar, allowing the Raptor to operate without leaks.

But this reduced thrust would also mean the SuperHeavy/Starship could carry less payload. I estimate a drop in payload to ca. 100 tons reusable. In such a scenario, the 16 refueling launches needed for a Starship HLS would be increased to 24 launches.

**Throttle Down Calculated by Acceleration Graph.**

A completely separate argument allows us to conclude the thrust was throttled down to less than 75%. This observer @meithan42 looked at the velocity and altitude data and derived the acceleration data.

On the acceleration graph I marked where the horizontal acceleration visually appears about 10 m/s

^{2}. The vertical acceleration there visually appears as about 6 m/s^{2}. Visually this occurs at about the 90 second point. Note that gravity subtracts ~10 m/s

^{2}from the vertical acceleration, the actual vertical acceleration produced by the engines thrust is about 16 m/s^{2}. Then the actual acceleration generated by the engines thrust is SQRT(10^{2}+ 16^{2}) = 18.87 m/s^{2}. But now lets calculate the actual acceleration that should be produced by the engines assuming they were running at full throttle at the 90 second point. The thrust is, (thrust) = (exhaust speed) * (flow rate). Since we are near vacuum the Isp will be 363 s and the exhaust speed 363*9.81 = 3,560 m/s. Then the thrust at full throttle with a total prop flow rate of 23,000 kg/s, should be thrust = 3,560*23,000 = 81,880,000 N.

We'll take the total mass of the rocket as 4,850,000 considering the tanks are filled slightly less than 100%. If the engines are at full throttle then the mass after 90 seconds is 4,850,000 - 90*23,000 = 2,780,000, and the actual acceleration generated would be 81,880,000/2,780,000 = 29.45 m/s

^{2}. This is well beyond amount observed. In contrast, if we take the throttled down propellant flow rate as 17,000 kg/s, then we calculate the actual acceleration as:

363*9.81*17,000/(4,850,000 - 90*17,000) = 18.23 m/s

^{2},a value much closer to what is actually observed. Robert Clark

## 4 comments:

Even simpler, given the acceleration graph starts at about 1.2G. It would imply engines are really outputting about 175t of thrust at liftoff.

Looking at fuel graph, if its even accurate, there is no sign of throttle back at max Q. The flatened acceleration could be all aerodynamics.

What I hear from the ground testing at the McGregor site (6 miles from my front porch) is no more Raptor starts at full power. I suspect they may have learned the hard way not to do that. -- GW

Thanks for that. When SpaceX tests a Raptor and it fails, it's often described as "testing it to failure". But for all we know this might be happening just when it is run at 100% power.

Bob Clark

If there is a problem with Raptor burning full duration at full thrust, it would make sense to operate the engines at full thrust for liftoff, while the vehicle is heaviest, to get better kinematics right off the pad to lower gravity losses. That would be T/W ~ 1.5, where 1.2 is rather inefficient. Actually, it would make sense to do that anyway, as once past max q, the trajectory is already bending over significantly, and pushing upward against the weight is rapidly becoming less of an issue than just obtaining pathways acceleration. Early on, as the weight decreases, you throttle back, probably somewhere near max q on the way up. Once moving transonic with the trajectory bending over, the vehicle is in an acceleration regime where max thrust is less important than just having adequate thrust. -- GW

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