SpaceX FH: STP-2 : LC-39A : June 25, 2019 - DISCUSSION

[Pete]

Guys, you cannot just plug in earth-surface kinematic equations and expect accuracy.
For one example, the value of "g" at 250km is a good 7% less than at the surface.

Rather than try to compensate for each of the oddities, just approach the problem using *orbital* equations?
It should be quite easy to determine the exact shape of an orbit, given known velocity , direction and altitude at a point on this orbit. Just calculate the Apogee of that orbit to know how high the stage will be at max.

The fact that a very big part of the orbit will lie below the surface of the earth is not relevant, as long as the body in question does not actually interact with that surface. i.e. valid until it hits atmosphere.

[Alexphysics]

Guys, you cannot just plug in earth-surface kinematic equations and expect accuracy.
For one example, the value of "g" at 250km is a good 7% less than at the surface.

Rather than try to compensate for each of the oddities, just approach the problem using *orbital* equations?
It should be quite easy to determine the exact shape of an orbit, given known velocity , direction and altitude at a point on this orbit. Just calculate the Apogee of that orbit to know how high the stage will be at max.

The fact that a very big part of the orbit will lie below the surface of the earth is not relevant, as long as the body in question does not actually interact with that surface. i.e. valid until it hits atmosphere.

And that's why I used the energy conservation equation. The term vi^2 - vf^2 gives just the radial velocity squared so it doesn't matter if the speed on the webcast is relative to the surface because it cancels on the formula. You only need to estimate the vertical speed and know the distance to the center of Earth at MECO and you get rf which would be the apogee of the orbit relative to the center of the earth.

[mn]

When would the stage abort a landing and how would it know when to do so?

I don't know how SpaceX implements it, but if I were to design it, instead if trying to cope with many different possible damage models and their expected symptoms, I'd go by a simple criteria similar to the autonomous LAS:

Constantly check whether the vehicles position, velocity and attitude is within a safe corridor to make a safe landing. Try the best to stay within this corridor with whatever actuators are available.

The stage would have done exactly that, and while still going fast enough for grid fins having sufficient control authority over a malfunctionibg TVC, it was seemingly spot on, definitely within the corridor.

The corridor can be calculated dynamically. It would simply be the space from which in an intact, functioning stage has sufficient control authority to make a succesful landing. If you ever go outside of that, you know you can't possibly make it anymore.

The corridor becomes narrower and narrower towards touchdown. At the same time any issue with TVC would become worse due to decreasing grid fin authority.

We did not see the stage in that phase, but my guess is the attitude rate and/or horizontal speed became too high, it left the corridor, knew it wouldnt make it and throttled up for the emergency fallback (safe ocisly)

That would look pretty much the same regardless of the exact type of failure or its cause.

Here is what I don't understand and why I question the intentional divert.

What exactly do you mean by 'knew it wouldn't make it'.

I see two possibilities.

1. If your calculations show that you will hit the target, continue adjusting thrust and hope you hit the target very softly.

2. If your calculations show that you will miss the target, there is no need to divert, you already missed.

[emerrill]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

[mn]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

Yes I understand that it could have this and it could have that.

I wouldn't decide to throw 50mil overboard because it might not land safely.

[emerrill]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

Yes I understand that it could have this and it could have that.

I wouldn't decide to throw 50mil overboard because it might not land safely.

True. Although the barge is worth more than the sticker price. If you take it out of commission, you affect your ability to recover boosters from future missions. At least til they get a second one operational.

[intelati]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

Yes I understand that it could have this and it could have that.

I wouldn't decide to throw 50mil overboard because it might not land safely.

True. Although the barge is worth more than the sticker price. If you take it out of commission, you affect your ability to recover boosters from future missions. At least til they get a second one operational.

Opportunity cost. In this case, I think a 50% chance of a successful landing is more than enough chance of failure to divert and save the barge. (Thus allowing you to catch other boosters in a timely manner)

[envy887]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

Yes I understand that it could have this and it could have that.

I wouldn't decide to throw 50mil overboard because it might not land safely.

Without center engine TVC, the probability of landing successfully is likely near zero. Especially if the engine is stuck hard over like the grid fins were on B1050.

At that point, the choice is pretty much either hit and damage the barge and lose the core anyway, or throw away the core and hope it misses the barge.

[mn]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

Yes I understand that it could have this and it could have that.

I wouldn't decide to throw 50mil overboard because it might not land safely.

Without center engine TVC, the probability of landing successfully is likely near zero. Especially if the engine is stuck hard over like the grid fins were on B1050.

At that point, the choice is pretty much either hit and damage the barge and lose the core anyway, or throw away the core and hope it misses the barge.

If the chances of landing are near zero it means you didn't need to divert, you were already in the water (mathematically).

I'm not suggesting that you can land with a failed TVC, I am only questioning that this was an 'intentional' divert.

Edit to add: Why would you 'hit and damage the barge'? TVC effects your ability to hit a particular target, not how hard you will hit it, You either land softly or hit the ocean. I'm looking for a scenario where a failed TVC will cause you to hit the barge but hard rather than soft. (Oh I'm sure we can contrive a scenario, definitely possible, but I think too farfetched to believe this was by design)

[envy887]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

Yes I understand that it could have this and it could have that.

I wouldn't decide to throw 50mil overboard because it might not land safely.

Without center engine TVC, the probability of landing successfully is likely near zero. Especially if the engine is stuck hard over like the grid fins were on B1050.

At that point, the choice is pretty much either hit and damage the barge and lose the core anyway, or throw away the core and hope it misses the barge.

If the chances of landing are near zero it means you didn't need to divert, you were already in the water (mathematically).

I'm not suggesting that you can land with a failed TVC, I am only questioning that this was an 'intentional' divert.

Edit to add: Why would you 'hit and damage the barge'? TVC effects your ability to hit a particular target, not how hard you will hit it, You either land softly or hit the ocean. I'm looking for a scenario where a failed TVC will cause you to hit the barge but hard rather than soft. (Oh I'm sure we can contrive a scenario, definitely possible, but I think too farfetched to believe this was by design)

Review the CRS-6 landing attempt. A small stiction delay in the thrust vector system controls caused the booster to land with excess horizontal velocity and tip over hard on the barge.

[mn]

It may calculate a probability of success or soemthing similar. Not everything is black and white.

It also could have determined it wouldn't have the fuel to complete the soft touchdown.

Yes I understand that it could have this and it could have that.

I wouldn't decide to throw 50mil overboard because it might not land safely.

Without center engine TVC, the probability of landing successfully is likely near zero. Especially if the engine is stuck hard over like the grid fins were on B1050.

At that point, the choice is pretty much either hit and damage the barge and lose the core anyway, or throw away the core and hope it misses the barge.

If the chances of landing are near zero it means you didn't need to divert, you were already in the water (mathematically).

I'm not suggesting that you can land with a failed TVC, I am only questioning that this was an 'intentional' divert.

Edit to add: Why would you 'hit and damage the barge'? TVC effects your ability to hit a particular target, not how hard you will hit it, You either land softly or hit the ocean. I'm looking for a scenario where a failed TVC will cause you to hit the barge but hard rather than soft. (Oh I'm sure we can contrive a scenario, definitely possible, but I think too farfetched to believe this was by design)

Review the CRS-6 landing attempt. A small stiction delay in the thrust vector system controls caused the booster to land with excess horizontal velocity and tip over hard on the barge.

Yes I've seen all the tip over videos, the barge didn't seem to care.

[Coastal Ron]

Well, IMO, "most likely" doesn't translate into "that's what it did."  It *might* have, but think about it: how can you tell from an external video source if the pitch over was a commanded response or just a result of the failure itself?

Echoing what Herb Schaltegger said, you are arguing that Elon Musk knows less about what happened than you do. And while I'm sure Elon Musk is working with imperfect information, he does have the advantage in knowing what the failure modes are for the Falcon 9 1st stage.

If S1 *did* abort, then I'd re-examine the criteria for an abort.  It appeared that the vertical velocity was right on target for an attempted landing, so if it did fail on landing the damage to ASDS would be no worse than any other failed landing attempt.

I disagree. I think their decision tree is very specific, and if they detect that part of their critical systems are not working properly then they trigger an abort. Why? Because out of all of the potential scenarios that could happen when critical systems fail during decent, very few would result in the recovery of a usable 1st stage.

And remember decisions have to be made on a split second basis, because the stage is coming in literally "Hot and Heavy".

The only reason to proceed with a landing attempt is if there is a high degree of potential success, because the vast amount of other scenarios result in financial penalties - costs to repair the ASDS, or possibility to have to replace the ASDS entirely. And other than stripping parts off of damaged stage, a damaged stage is no longer an asset, it is a liability.

My $0.02

[RonM]

When would the stage abort a landing and how would it know when to do so?

I don't know how SpaceX implements it, but if I were to design it, instead if trying to cope with many different possible damage models and their expected symptoms, I'd go by a simple criteria similar to the autonomous LAS:

Constantly check whether the vehicles position, velocity and attitude is within a safe corridor to make a safe landing. Try the best to stay within this corridor with whatever actuators are available.

The stage would have done exactly that, and while still going fast enough for grid fins having sufficient control authority over a malfunctionibg TVC, it was seemingly spot on, definitely within the corridor.

The corridor can be calculated dynamically. It would simply be the space from which in an intact, functioning stage has sufficient control authority to make a succesful landing. If you ever go outside of that, you know you can't possibly make it anymore.

The corridor becomes narrower and narrower towards touchdown. At the same time any issue with TVC would become worse due to decreasing grid fin authority.

We did not see the stage in that phase, but my guess is the attitude rate and/or horizontal speed became too high, it left the corridor, knew it wouldnt make it and throttled up for the emergency fallback (safe ocisly)

That would look pretty much the same regardless of the exact type of failure or its cause.

Here is what I don't understand and why I question the intentional divert.

What exactly do you mean by 'knew it wouldn't make it'.

I see two possibilities.

1. If your calculations show that you will hit the target, continue adjusting thrust and hope you hit the target very softly.

2. If your calculations show that you will miss the target, there is no need to divert, you already missed.

3. If your calculations show that you will hit the target, but outside the parameters for a safe landing, divert.

[Vettedrmr]

Well, IMO, "most likely" doesn't translate into "that's what it did."  It *might* have, but think about it: how can you tell from an external video source if the pitch over was a commanded response or just a result of the failure itself?

Echoing what Herb Schaltegger said, you are arguing that Elon Musk knows less about what happened than you do.

Huh??  Of *course* Elon has more knowledge than I do.  It's absurd to think otherwise.  I was quoting Elon, who said it was "most likely" that the stage aborted the landing.  "Most likely" does not translate well into the English language as "Yes".  It's a statement of probability, not a certainty.  I expect that SpaceX now knows exactly what the stage did, but as best I know nothing beyond Elon's original tweet has been published.

I disagree. I think their decision tree is very specific, and if they detect that part of their critical systems are not working properly then they trigger an abort. Why? Because out of all of the potential scenarios that could happen when critical systems fail during decent, very few would result in the recovery of a usable 1st stage.

That's a good point.

And remember decisions have to be made on a split second basis, because the stage is coming in literally "Hot and Heavy".

The control system is running at its normal rate throughout the landing sequence (at least we never changed our execution frame rate during operations).

The only reason to proceed with a landing attempt is if there is a high degree of potential success, because the vast amount of other scenarios result in financial penalties - costs to repair the ASDS, or possibility to have to replace the ASDS entirely. And other than stripping parts off of damaged stage, a damaged stage is no longer an asset, it is a liability.

My $0.02

That's another good point.  My main reason was to try to save the data recorder and any other evidence for the investigation.  However, their telemetry may have enough bandwidth that they don't use data recorders.

Have a good one,
Mike

[Barley]

Here is what I don't understand and why I question the intentional divert.

What exactly do you mean by 'knew it wouldn't make it'.

I see two possibilities.

1. If your calculations show that you will hit the target, continue adjusting thrust and hope you hit the target very softly.

2. If your calculations show that you will miss the target, there is no need to divert, you already missed.

The "target" is not just a position.  It's a position, and a velocity, and an orientation and an angular velocity.  There are a lot of cases where you can be sure that it will both hit the barge and disassemble.  In those cases it would make sense to divert.

[Barley]

And other than stripping parts off of damaged stage, a damaged stage is no longer an asset, it is a liability.

A (moderately) damaged stage could be quite valuable to the engineering team doing failure analysis, far beyond the value of strippable parts.

[cscott]

Elon/SpaceX might be just getting the telemetry recordings now, with the arrival of Ms. Tree in port.  That assumes Ms. Tree captured non-fairing telemetry or rendezvoused with another Go sister before sprinting back to port.  They may be waiting for the rest of the fleet to reach port to deliver the recorded telemetry from the center core.

[vanoord]

I see two possibilities.

1. If your calculations show that you will hit the target, continue adjusting thrust and hope you hit the target very softly.

2. If your calculations show that you will miss the target, there is no need to divert, you already missed.

As I understand it, when an aeroplane is on a landing approach it has to come in between two lines, one high and one low. If it goes outside those, the landing has to be aborted.

The original suggestion that the core comes down into what's effectively a cone would be a valid way to programme the stage to abort - if it goes outside pre-determined parameters, it throttles up and ends up somewhere other than the drone ship.

The more simple answer is that a TVC failure caused the stage to veer off-target and what we saw was a doomed attempt to correct it.

[LouScheffer]

Guys, you cannot just plug in earth-surface kinematic equations and expect accuracy.
For one example, the value of "g" at 250km is a good 7% less than at the surface.

Rather than try to compensate for each of the oddities, just approach the problem using *orbital* equations?
It should be quite easy to determine the exact shape of an orbit, given known velocity , direction and altitude at a point on this orbit. Just calculate the Apogee of that orbit to know how high the stage will be at max.

The reason you might want to compensate for each of the oddities is that then you can do the computation in one line on a calculator.  The pure physics solution you suggest is called Lambert's problem and has no closed form solution.  All known solutions require iterations and mathematicians have been arguing about the best way to solve it for centuries.

Furthermore, the three main tweaks get very close to the right answer.  They are:
  (a) Gravity is weaker higher up, by about 0.5 m/s at 150 km
  (b) The forward velocity generates an additional acceleration of v^2/r in the Earth frame.  For this you need the inertial velocity, not the rotating frame velocity shown in the SpaceX webcast (I made this mistake above).  This means the horizontal velocity is about 400 m/s faster than the SpaceX numbers.  Plugging in 3200 m/s horizontal and Earth's radius gives 1.58 m/s^2.
  (c) The Earth is not flat.  This effect is small (the landing location is about 2 km below a plane defined by the start of coast location).  Since we are guessing the 60 km altitude for start of entry burn anyway, this can be ignored.

So with these tweaks, we should use an effective g of 9.8 - 0.5 - 1.58 = 7.72 m/s.  Knowing the 370 second coast, the 123 km start altitude, and the 60 km end altitude, then we solve for 123000 + v*t - 1/2*g*t = 60000, to get vertical v = 1257 m/s.  This is within 1% of the correct value of 1265 m/s, as determined by the physics based computation below (in Python).  The estimated peak altitude is 226.6 km as opposed to the correct 225.6 km.  So the few tweaks get a result that is likely more accurate than the input data we are using.

import math
Re = 6356000            # Radius of Earth in meters
mu = 3.985744e14        # Gravitational constant of Earth
Erot = 40000000/86400.0*math.cos(28.5/180.0*math.pi)  # Rotation speed of earth at 28.5 degrees north
x = 0;
y = Re+123000           # Initial altitude is 123 km
vy = 1265.0             # Initial vertical velocity (tweak this to get right result)
vx = math.sqrt(3079**2 - vy**2)  # Initial velocity in Earth-rotating frame is 3079 m/s, find X component
vx += Erot                       # Add Earth's rotation to convert to velocity in inertial frame
print("vx = ", vx, "Earth rotation added", Erot, "m/s")
r = math.sqrt(x**2+y**2)
t = 0
dt = 0.1
while t < 370-dt/2:
  a = mu/r**2           # Find the acceleration magnitude
  ax = a * (x/r)        # Find x and y components
  ay = a * (y/r)
  vx = vx - ax*dt       # Update velocity = integral of acceleration
  vy = vy - ay*dt
  x = x + vx*dt         # Update position, integral of velocity (in inertial space)
  y = y + vy*dt
  t += dt
  r = math.sqrt(x**2+y**2)
  theta = math.pi/2 - math.atan(y/x)  # angle from vertical
  dr = Re*theta - Erot*t              # distance downrange, compensation for Earth rotation
  print("t={0:5.1f} g={1:6.4f} m/s^2  dr={2:8.3f} km  y={3:8.3f} alt={4:8.3f}".format(t,a, dr/1000.0, y/1000.0, (r - Re)/1000.0))

[jpo234]

https://twitter.com/nasawatch/status/1144332878026641408

In this #satellite image from June 26th, you can see Falcon Heavy's two side boosters at @SpaceX's Landing Zones 1 & 2 at Cape Canaveral from the June 25th STP-2 mission. spacex.com/webcast

OK, I know I need glasses, but where are the boosters?

Here, I think.