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Commercial and US Government Launch Vehicles => Blue Origin => Topic started by: Stan-1967 on 10/18/2016 07:51 am

Title: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Stan-1967 on 10/18/2016 07:51 am
 
I'm trying to guess, or understand, why Blue Origin went with 6 landing legs in their renderings.  ( not sure I count them right)  I'll save my guess for last, but here is the trail of cookie crumbs I've been following.

1.  When SpaceX started landing attempts, there was discussion of how many legs are optimum.  3 is the obvious minimum.  4 is better, but if one breaks, as happened on a barge landing, it fails.  5 then could be made stable in the instance of 1 leg failing.   SpaceX settled on 4, as they tested everything out.

2.  Blue Origin then enters the picture with New Shepard, which also uses 4 legs.   So it looks like a good confirmation of going with 4. 

3.  Not that "style" matters when it comes to engineering design, but it was noticed by poster "Robotbeat", that New Shepard has a distinctly Bacteriophage T4 virus look to it operation.  Humorous, but apt!  Engineering departments worldwide have eagerly been studying the natural world for inspiration in design.  It's highly likely some of the engineers at Blue have been exposed to this.  Coincidence?  Y/N?

4.  Along comes New Glenn with 6 legs. WHY 6?  It doesn't add stability.  It's over redundant for load bearing.  It's more moving parts and things to fail, its more complicated.

5.  SpaceX unveils ITS, and it looks like there will be zero legs on the booster, it will land in it's launch cradle.

So a big divergence is going on between Blue's thinking and SpaceX.   But they are trying to solve the same problem.  How to move towards rapid & economic reuse of rockets?  SpaceX's choice is obvious in how it will accomplish that. It also seems unforgiving & much more technically challenging, but it they ever pull it off, it can't get much more simple.

Blue Origin on the other hand is looking at 6 legs.  So this rambling introduction of a thread now concludes with my speculation as to WHY 6 legs:

With 6 legs, the New Glenn Booster could be built to articulate those legs in a hexapod locomotive arrangement, alternating between 3 legs and 3 legs,  to walk itself back to it's launchpad.  The empty booster doesn't weigh that much that a portable power truck couldn't drive up next to it to supply hydraulic or pneumatic power to move the whole machine.   It also lends itself to vertical integration on the pad, which would be efficient. 

A time lapse movie of New Glenn walking itself across the launch complex would be fantastic!

So for this thread, what are other thoughts on the need for 6 legs? What do you think of my "Hexapod Locomotive" conjecture?


(edited to 6 legs..thought I counted 7 at one point )
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: gwiz on 10/18/2016 09:48 am
Assuming the engine arrangement is six outboard and a single centre one, the reason could be structural with the legs using the same points as the engines to feed the load into the vehicle.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: hkultala on 10/18/2016 09:54 am
1)

6 means it can an be symmetrical with the 6 engines. Something else than 3 or 6 would mean much more complex mechanical structures.

2)

6 means there is redundancy. on the legs. One leg can fail totally and it's still stable. At least 5 legs needed for this, but 5 would be bad for symmetry. At least one F9 1st stage landing failed due failing leg, so the redundancy can be important.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Jim on 10/18/2016 12:45 pm

What do you think of my "Hexapod Locomotive" conjecture?


No way that is happening.  The number of legs reduces the loads by each individual leg and hence the attach point structure on the vehicle. 
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Norm38 on 10/18/2016 02:19 pm
A fun idea, but too "Star Wars" to be real.  The 6 legs will have one degree of freedom, likely latch open and be built as light as possible.  The actuators and complex rotating joints to allow 2-3 degrees of freedom for walking would add far too much weight.

Maybe after landing the legs could be lifted one at a time and set down on wheeled bogeys?  Then once all legs are up on wheels, a tug pulls it?
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Stan-1967 on 10/18/2016 03:03 pm

What do you think of my "Hexapod Locomotive" conjecture?


No way that is happening.  The number of legs reduces the loads by each individual leg and hence the attach point structure on the vehicle.

100% sure?  That's an early thread killer.

I do agree that the thrust structure loading with the 6 outer ring engines is the much more highly likely reason for the 6 leg choice.  ( use common load paths)

1.  Is there a imperative to configure the rocket to reduce or eliminate ground support equipment needed to prep the rocket for it's next launch?  Any estimates on what it costs to bring F9 horizontal after a barge landing vs. on the pad?

2.  Is there going to be a fundamental shift with New Glenn or ITS that the boosters home is on the launch pad. (manifest permitting) if flight rates ever get high?  Current flight rates put no pressure on the slow turnaround of F9, so for now, nothing is pressing a dramatic new capability.

I haven't read much about what vehicle integration for New Glenn may look like, as I don't think they have hinted at anything.  SpaceX's video for ITS is solidly in the vertical integration camp.

Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: RonM on 10/18/2016 03:23 pm
Added mass to turn the landing gear into hexapod locomotion would reduce payload. Increasing complexity increases cost and reduces reliability.

Best to keep the ground support equipment on the ground.

Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Clf on 10/18/2016 03:51 pm
By raising a leg a time it's possible to load the booster on a movable structure without the need to have a large  crane in place and in reach of the landed booster. This may simplify and accelerate a lot  ground operations to me. 
c
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Stan-1967 on 10/18/2016 04:20 pm
Added mass to turn the landing gear into hexapod locomotion would reduce payload. Increasing complexity increases cost and reduces reliability.

Best to keep the ground support equipment on the ground.

You may be right, you may be wrong.  There is no baseline of knowledge to weigh the advantages vs. disadvantages for this case.  The few cases of reuse that have been attempted ( STS ) ended up being very expensive.  Even F9 doesn't look too efficient in all the time, labor, & equipment needed to barge land, take the returned vehicle from vertical to horizontal, transport it & integrate a new payload.   

In this case, the advantage is enabling rapid reuse by quickly returning the rocket to the pad for another launch.   Is it worth it?  What does it cost vs. the alternatives? 

Every addition of a features to a rocket that make it reusable ( legs, fins, multiple engines) is less mass efficient, & reduce the payload compared to an expendable vehicle, & increase complexity.   The requirements for reuse then push the size of the rocket to be bigger & more costly.  Your logic dismisses all of these options because they reduce payload, and yet multiple companies are out there pushing for reusable rockets. Why?

In the end, reuse is judged economically by adding up all the extra costs that amortize over N# launches against the cost of expendable.  A walking hexapod rocket would be no different.  You would tally all costs associated with adding more degrees of freedom into the mechanics of the legs, as well as any other ground equipment needed, and compare against the alternative.   

Finally, I see no requirement that all the hydraulics and power generator to articulate this hexapod concept be contained in the rocket.  What is required is that each leg has enough degrees of freedom to articulate the CG within a tight range of motion.  The mass intensive parts of a hydraulic system ( working fluid, pumps, generators) can be contained in mobile GSE.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Patchouli on 10/18/2016 04:41 pm
1)

6 means it can an be symmetrical with the 6 engines. Something else than 3 or 6 would mean much more complex mechanical structures.

2)

6 means there is redundancy. on the legs. One leg can fail totally and it's still stable. At least 5 legs needed for this, but 5 would be bad for symmetry. At least one F9 1st stage landing failed due failing leg, so the redundancy can be important.


Pretty much and as in other posts would allow load paths to be shared with the engines.

As for people saying making it a hexapod walker it wouldn't be practical though I could see them making it where one leg can be lifted at a time so wheeled transporters could be placed under each one.
Kinda like what's in this video.
https://www.youtube.com/watch?v=wL3YvOe0ZgE
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: RonM on 10/18/2016 05:41 pm
Added mass to turn the landing gear into hexapod locomotion would reduce payload. Increasing complexity increases cost and reduces reliability.

Best to keep the ground support equipment on the ground.

You may be right, you may be wrong.  There is no baseline of knowledge to weigh the advantages vs. disadvantages for this case.  The few cases of reuse that have been attempted ( STS ) ended up being very expensive.  Even F9 doesn't look too efficient in all the time, labor, & equipment needed to barge land, take the returned vehicle from vertical to horizontal, transport it & integrate a new payload.   

In this case, the advantage is enabling rapid reuse by quickly returning the rocket to the pad for another launch.   Is it worth it?  What does it cost vs. the alternatives?

Turning a rocket into a legged robot won't help with a barge landing. Like any other cargo, a crane is the best way to get the stage off of a barge.

A little industrial engineering would improve the SpaceX process by improving crane operations. Nothing wrong with transporting a stage horizontally.

Every addition of a features to a rocket that make it reusable ( legs, fins, multiple engines) is less mass efficient, & reduce the payload compared to an expendable vehicle, & increase complexity.   The requirements for reuse then push the size of the rocket to be bigger & more costly.  Your logic dismisses all of these options because they reduce payload, and yet multiple companies are out there pushing for reusable rockets. Why?

No, my logic doesn't dismiss reusability. To make a rocket reusable you add what is necessary. Your lack of logic assumes it's a good idea to add unnecessary items to a rocket.

In the end, reuse is judged economically by adding up all the extra costs that amortize over N# launches against the cost of expendable.  A walking hexapod rocket would be no different.  You would tally all costs associated with adding more degrees of freedom into the mechanics of the legs, as well as any other ground equipment needed, and compare against the alternative.   

Finally, I see no requirement that all the hydraulics and power generator to articulate this hexapod concept be contained in the rocket.  What is required is that each leg has enough degrees of freedom to articulate the CG within a tight range of motion.  The mass intensive parts of a hydraulic system ( working fluid, pumps, generators) can be contained in mobile GSE.

Having to add the hydraulics and power after the rocket lands will take time, effort, and of course money. It would be easier and quicker to use a crane and transport vehicle.

It's obvious that this idea would cost more than current landing operations.

It might have some merit if the landing pad was on the Moon or Mars. There are no cheap cranes and transporters available off planet.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Stan-1967 on 10/18/2016 06:29 pm

1.  Turning a rocket into a legged robot won't help with a barge landing. Like any other cargo, a crane is the best way to get the stage off of a barge.

2.  ...To make a rocket reusable you add what is necessary. Your lack of logic assumes it's a good idea to add unnecessary items to a rocket.

3.  Having to add the hydraulics and power after the rocket lands will take time, effort, and of course money. It would be easier and quicker to use a crane and transport vehicle.

4.  It's obvious that this idea would cost more than current landing operations.

5.  It might have some merit if the landing pad was on the Moon or Mars. There are no cheap cranes and transporters available off planet.


1.  Has Blue said they will land New Glenn on a barge? RTLS?  No they have not.  Can New Glenn land and be stable on a small barge, or will it need to scale up to something much bigger and more expensive?  You are assuming facts without evidence.   Do you have inside information on SpaceX cost for barge, labor, storage, etc?

2.  I am not assuming it is a good idea.  I think it is possible to make it happen, but there is no basis either way to say if its better or worse without knowing specific costs.

3.  Again, you don't know any of this.   It has taken over a week to get an F9 off a barge and back to horizontal storage.  A walker articulating 1m/min could have the rocket back at the launchpad in less than a day if doing a a RTLS closeby.  Everything takes time and money, so that fact is not a reason to do nothing.  Do what is efficient.

4.  It is not obvious.  What is your cost data that makes this obvious? 

5.  So you like the idea then!
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Lars-J on 10/18/2016 06:40 pm
This is clearly an idea that Stan-1967 likes a lot, and nothing is going to change his mind.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Stan-1967 on 10/18/2016 07:09 pm
This is clearly an idea that Stan-1967 likes a lot, and nothing is going to change his mind.

I do like the idea if it enables rapid reuse, & is technically possible.  I am agnostic to this solution vs. any other solution when compared against cost and efficiency.

Dismissing ideas out of hand without any data, or pretending that optimal solutions to new problems  (i.e reuse) are known, when they are clearly not, is boring and unimaginative.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: RonM on 10/18/2016 07:36 pm

1.  Turning a rocket into a legged robot won't help with a barge landing. Like any other cargo, a crane is the best way to get the stage off of a barge.

2.  ...To make a rocket reusable you add what is necessary. Your lack of logic assumes it's a good idea to add unnecessary items to a rocket.

3.  Having to add the hydraulics and power after the rocket lands will take time, effort, and of course money. It would be easier and quicker to use a crane and transport vehicle.

4.  It's obvious that this idea would cost more than current landing operations.

5.  It might have some merit if the landing pad was on the Moon or Mars. There are no cheap cranes and transporters available off planet.


1.  Has Blue said they will land New Glenn on a barge? RTLS?  No they have not.  Can New Glenn land and be stable on a small barge, or will it need to scale up to something much bigger and more expensive?  You are assuming facts without evidence.   Do you have inside information on SpaceX cost for barge, labor, storage, etc?

2.  I am not assuming it is a good idea.  I think it is possible to make it happen, but there is no basis either way to say if its better or worse without knowing specific costs.

3.  Again, you don't know any of this.   It has taken over a week to get an F9 off a barge and back to horizontal storage.  A walker articulating 1m/min could have the rocket back at the launchpad in less than a day if doing a a RTLS closeby.  Everything takes time and money, so that fact is not a reason to do nothing.  Do what is efficient.

4.  It is not obvious.  What is your cost data that makes this obvious? 

1, 2, 4. It's not my job to provide numbers that disprove your idea. It's your job to provide numbers to prove it.

Boring old tech like cranes and trucks are cheap. I don't need to see SpaceX expense sheets to know that.

3. Currently, SpaceX is in no hurry to move a returned stage. It's not like they are going to launch it the next day. In the future, with improve processes, they can speed up the process.

Maybe after landing the legs could be lifted one at a time and set down on wheeled bogeys?  Then once all legs are up on wheels, a tug pulls it?

That sounds like a good idea.

5.  So you like the idea then!

5. While I don't think it's a practical idea, it is pretty cool.  :)
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Kryten on 10/18/2016 08:52 pm
1.  Has Blue said they will land New Glenn on a barge? RTLS?  No they have not.
Yes they have. To directly quote from Blue's planning application for the CCAFS pad;
Quote
Present plans call for returning first stages for a landing on a downrange ocean-going platform, and return it to a facility for reuse.
[...]
After a successful launch the first stage would return to the Earth for recovery in the Atlantic Ocean approximately 750 nautical miles downrange in the Atlantic Ocean, east of and well off the Carolina coast, and any payload or capsule would land under parachute at a yet to be determined land site in Texas.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Stan-1967 on 10/18/2016 11:01 pm
1.  Has Blue said they will land New Glenn on a barge? RTLS?  No they have not.
Yes they have. To directly quote from Blue's planning application for the CCAFS pad;
Quote
Present plans call for returning first stages for a landing on a downrange ocean-going platform, and return it to a facility for reuse.
[...]
After a successful launch the first stage would return to the Earth for recovery in the Atlantic Ocean approximately 750 nautical miles downrange in the Atlantic Ocean, east of and well off the Carolina coast, and any payload or capsule would land under parachute at a yet to be determined land site in Texas.

You are correct. I had missed that, & thought RTLS was still on the table. 
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Jim on 10/19/2016 12:09 am

Dismissing ideas out of hand without any data, or pretending that optimal solutions to new problems  (i.e reuse) are known, when they are clearly not, is boring and unimaginative.


Throwing stuff against the wall and seeing if it sticks is childish.  Some basis thought has to be put into ideas.
It is easy to dismiss ideas when they fail the eye test.    This is a prime example of a solution looking for a problem.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Stan-1967 on 10/19/2016 01:36 am

Dismissing ideas out of hand without any data, or pretending that optimal solutions to new problems  (i.e reuse) are known, when they are clearly not, is boring and unimaginative.


Throwing stuff against the wall and seeing if it sticks is childish.  Some basis thought has to be put into ideas.
It is easy to dismiss ideas when they fail the eye test.    This is a prime example of a solution looking for a problem.

I was not aware that all the problems, both economic & technical, of rocket reuse had been solved with such certainty as to preclude a possible alternative from mere discussion. 

Suggesting I see this as a solution looking for a problem is an inversion of ordering. I know my intent, you do not.  Casting aspersions to my motives is unnecessary to discredit it if it is no value or unworkable.

My basis in thought is that re-use is not as easy or cheap as it's advocates had hoped.  I see a huge basis of thought put into the RTLS & DPL maneuver, as it is the first order problem of reuse.  What I see from SpaceX & Blue after the rocket has landed looks just put together from what can be made to work.  None of it was designed, & it is not rapid. At this early stage for both players, cant' say they should be doing anything different.  Where all this ends up is unknown at this point. 
 
I did not post it for validation or giggles.  I like to challenge conventional thinking, and I have not heard a show stopping reason that a large rocket than can land near it's pad could not also walk itself back to the launcher for rapid re-use.  I applied that thought New Glenn, as well as rapid re-use in general.

I understand that just because something can be done, doesn't mean it should be.  But to never ask is to never learn why.

Your "eye test" is an appeal to your own authority.  Which in this NSF space is substantial.  Even if correct, it is lazy reasoning on it's own.   
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Chasm on 10/19/2016 02:12 am
Taking a look at the existing spaces & load bearing structures in a rocket design and then going with 6 legs is plausible. Walking rockets, not so much.

Rapid reuse is not required to reduce launch costs. Cheap reuse is. If a stage needs to spend x days or even weeks in transfer that should not be that expensive in itself, you "just" need more hardware in rotation.
That said a leg design that can be retracted at will goes a long way to make recovery and refurbish operations simpler and faster.

What I find more interesting is the small footprint of the deployed legs (~1.8x tank diameter) compared to the F9 (~5.6x ?), even smaller(!) than NS (~2x). Blue must be very certain that they can land the stage perpendicular, with very small tipping moments. 
Given the offshore recovery plans downrange that makes me think less barge and more Sea Launch style platform. (Land on a platform, transfer on a ship with platform cranes, unload at launch site, repeat.)
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: TrevorMonty on 10/19/2016 02:45 am
I do wonder what payloads they plan to fly that demand downrange recovery. At estimated 50t expendable should still be good for 30t at RTLS or 40t downrange.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: leaflion on 10/19/2016 03:34 am
Taking a look at the existing spaces & load bearing structures in a rocket design and then going with 6 legs is plausible. Walking rockets, not so much.

Rapid reuse is not required to reduce launch costs. Cheap reuse is. If a stage needs to spend x days or even weeks in transfer that should not be that expensive in itself, you "just" need more hardware in rotation.
That said a leg design that can be retracted at will goes a long way to make recovery and refurbish operations simpler and faster.

What I find more interesting is the small footprint of the deployed legs (~1.8x tank diameter) compared to the F9 (~5.6x ?), even smaller(!) than NS (~2x). Blue must be very certain that they can land the stage perpendicular, with very small tipping moments. 
Given the offshore recovery plans downrange that makes me think less barge and more Sea Launch style platform. (Land on a platform, transfer on a ship with platform cranes, unload at launch site, repeat.)

How are you calculating landing footprint?
I'm guessing you are circumscribing a circle around the shape of the legs to get the footprint.  A better method is to inscribe a circle within the shape of the legs.  That will be your minimum tipover radius.  This the primary reason nobody has tried 3 legs, it requires really long legs to get a bigger tipover radius.  6 legs will get you a significantly larger tipover radius for the leg length than a 4 legged design would.  That said, 6 legged New Glenn still has a smaller tipover radius than a 4 legged F9

Some math: R=L cos (180/n)
where R=tipover radius, L=leg length, n=# of legs.

As n->infinity, R=L

With one leg not deployed, R=L cos (360/n)

Decide if you require fault tolerance, then optimize for weight.  That's how many legs you want.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Steven Pietrobon on 10/19/2016 04:48 am
Some math: R=L cos (180/n)
where R=tipover radius, L=leg length, n=# of legs.

Some calculations below.
n   R/L
3   0.5
4   0.707
5   0.809
6   0.866
7   0.901
8   0.924

My personal preference is five legs. That's the minimum number where you can have one leg fail and still be standing. Here's the probably of falling given probably of a leg failure is p = 1% = 0.01. With five legs there are five combinations of single leg and five combinations of dual leg failures that are survivable. Compared to four legs, we can reduce the failure rate from about 1 in 20 to about 1 in 2020. Six legs only goes down to 1 in 3250.

n  Pf  p=0.01
3  1-(1-p)^3 = 2.97%
4  1-(1-p)^4 = 4.94%
5  1-(1-p)^5 - 5p(1-p)^4 - 5p^2(1-p)^3 = 0.0495%
6  1-(1-p)^6 - 6p(1-p)^5 - 12p^2(1-p)^4 = 0.0308%
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Darkseraph on 10/24/2016 08:38 pm
Perhaps since it is landing on a barge out in the sea, that is not the most stable platform, having more points of contact has some advantage when landing. Or more legs allows shorter lighter structures; the span on this booster seems much less than Falcon 9.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Dante80 on 10/26/2016 06:40 am
Not only is New Glenn destined for barging - we've heard nothing about RTLS, but the hints we have from Blue are for landing much, much further from the launch pad than even the most energetic F9 GTO mission. I don't remember right now where this came from exactly (I think it was the DPL patent Blue did), but it is I think pretty credible.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: Chasm on 10/26/2016 07:53 am
We got a landing 750 nautical miles downrange from a launch site Drainage Analysis Technical Memorandum [PDF (https://permitting.sjrwmd.com/apps/idcplg?IdcService=GET_FILE&coreContentOnly=1&RevisionSelectionMethod=Latest&allowInterrupt=1&dDocName=EREG_6388327)]. Here is the relevant part:

Quote from: Drainage Analysis Technical Memorandum, page 1-4
After arrival at the Integration Facility, the 1st Stage and 2nd Stage, and a possible 3rd Stage, would then be mated together and integrated onto the Transporter Erector system. Following integration of the booster stages, the SV (or PA) would be attached, and then the entire system would undergo a readiness test. The OLV would then be transported from the Integration Facility to the Launch Pad and erected for launch. After a successful launch the first stage would return to the Earth for recovery in the Atlantic Ocean approximately 750 nautical miles downrange in the Atlantic Ocean, east of and well off the Carolina coast, and any payload or capsule would land under parachute at a yet to be determined land site in Texas.


More recently Jeff Bezos said during the 2016 Pathfinder Awards that landing will be on a ship. (Link to that moment (https://youtu.be/VNwE3sRWxHw?t=474))

Drawing a 750nm circle around the launch site "well of the Carolina Coast" can be as close as ~100nm short of Bermuda. (Or further south as close as ~200nm short of Puerto Rico.)
Should be interesting to see if they try something with that in the future.
Title: Re: New Glenn landed booster: Why 6 legs? Hexapod Locomotion?
Post by: ZachF on 11/25/2016 01:54 am
Some math: R=L cos (180/n)
where R=tipover radius, L=leg length, n=# of legs.

Some calculations below.
n   R/L
3   0.5
4   0.707
5   0.809
6   0.866
7   0.901
8   0.924

My personal preference is five legs. That's the minimum number where you can have one leg fail and still be standing. Here's the probably of falling given probably of a leg failure is p = 1% = 0.01. With five legs there are five combinations of single leg and five combinations of dual leg failures that are survivable. Compared to four legs, we can reduce the failure rate from about 1 in 20 to about 1 in 2020. Six legs only goes down to 1 in 3250.

n  Pf  p=0.01
3  1-(1-p)^3 = 2.97%
4  1-(1-p)^4 = 4.94%
5  1-(1-p)^5 - 5p(1-p)^4 - 5p^2(1-p)^3 = 0.0495%
6  1-(1-p)^6 - 6p(1-p)^5 - 12p^2(1-p)^4 = 0.0308%

They are probably using 6 legs because the it allows you to put the leg hardware in between the 6 outer rocket engines. 5 legs would need 5-6 engines (5 engine outer ring) and the rocket nozzle area ratio is pretty poor for such designs compared to 7 engines like NG.