On the other hand, density is mass per unit volume. Mass is mass regardless of gravity. Therefore, 1.3 g/cm2 is 1.3 g/cm2 on Earth, the moon, or anyplace else.
It looks like your example gives mass per unit area...
2nd revised calculations 18.8 total feet / 5 seconds = average of 3.76 feet 5 seconds at 3.76 feet or 114.15 cm from surface produces an area effected by exhaust to be 229 cm in diameter. An area of 41,187 cm2 Using equations provided in Reply #9 on Apr 5, 2011 44.438 x 1000 / 0.22 = 90,581 cm3 Depth = 90,581 / 41,187 = 2.20 cm (.87 inch) of Lunar soil would be propelled at 3000 m / sec from an area 229 cm (90 inches) in diameter.
Where did your number of 44.438 come from? If the soil velocity is 3000 m/s, then the soil mass should be,
m = 89676000 x 2 / 30002 = 19.928 kg
And if we use the correct density,
Volume = 19.928 x 1000 / 1.30 = 15329 cm3
Depth = 15329 / 41187 = 0.372 cm
Of course much of this is just hairsplitting. The method we're using is intended to do no more than provide a ballpark figure to see if it's reasonable to expect the formation of a large crater. Quibbling over whether the answer is 0.3 cm or 3 cm misses the point that neither result is a big conspicuous crater. The numbers simply don't support the expectation that a large crater should result.
Of course much of this is just hairsplitting. The method we're using is intended to do no more than provide a ballpark figure to see if it's reasonable to expect the formation of a large crater.
Yeah I've been sort of sitting on my hands here because it's fun watching Bob run numbers. The method here makes several important but perfectly valid simplifications, such as assuming uniform regolith density, uniform plume density, and ideal energy transfer. What we hope for here is a good order-of-magnitude estimation. We're looking at centimeters at most, so regardless of how you populate the estimates with reasonable values, your not going to get a deep hole. Professionally I would report these results as "0-5 cm expected erosion." The method Bob has chosen supports no greater precision.
What you really want is a scour model. Scouring occurs when you have (a) a moving fluid, (b) erosible elements, and (c) non-erosible elements. The patterns of fluid flow around non-erosible elements (rocks, the landing legs, the denser portion of the regolith etc.) effects a pattern of erosion and displacement in the erosible elements (loose regolith).
Scour, for example, describes the movement of river water around bridge piers and over the river bed, and of air around tall buildings situated in natural erosible environments. Typically rough material called rip-rap is used to break up the fluid flow and render it turbulent otherwise vortices and eddies form on the downstream side of the piers and scour away the supporting riverbed.
A scour model incorporates an erosibles model, in this case a distribution of particle sizes, shapes, and masses. Particle shape dictates mechanical cementation, which in turn dictates how fluid impingement produces a dynamic response. Rip-rap is commonly rough-hewn rock, but increasingly cast concrete shapes are being used. Particle mass and size (which are listed as distributions rather than considered uniform) determine particle entrainment response aside from cementation. Different distributions of particle size and shape have different aggregate results, and susceptibility to displacement through entrainment does not vary linearly with either. We borrow particle models from settling and piling-shear models.
A scour model incorporates a fluid dynamics model, in this case a compressible gas model of the exhaust plume. Exhaust plume models are problematic. The Navier-Stokes models either of compressible or non-compressible flow do not describe plume dynamics well inside the thrust chamber. However, for purposes of fluid impingement on a suitably distant surface, they do. In other words, combustion products inside a thrust chamber are not always fully Newtonian, but they become Newtonian a sufficient distance from the engine throat. For impingement on an erosible or irregular surface, turbulence must be modeled -- and the typical models do not account for this except through time-averaged values. Thus only large-scale fluid movement can be modeled, and this will necessarily fail to model centimeter-sized local turbulence effects. The fluid-dynamics model easily handles non-erosible obstacles as well as the compression of the fluid as it approaches the surface.
Having handwaved the basics of the problem, I can now tentatively say that this is a three-week modeling effort at a professional footing. I would bid this at right around $12,000 labor costs and $20,000 computer time, for $32,000. And I would expect to see a conical crater (deeper in the center, negligible at the edges) with a maximum depth of 3 cm.
The cheapness of Bob's solution is its reward. I highly doubt anyone wants to pay $32,000 for my refinement using best methods. Bob gave you a defensible answer for free.
Thrust is counteracting the gravitational force acting on the LM, that is, the LM's weight. Density is mass per unit volume. Weight and mass are not the same thing.
pounds = force grams = mass
Right. This constant confusion between pounds force and pounds mass is one of the many reasons I wish we could junk the traditional system of units once and for all and just use SI for everything.
You can minimize the confusion with traditional units by always stating "pounds-force" or "pounds-mass", but it's rarely done. Even rocket scientists screw up badly; the widespread notion of specific impulse measured in "seconds" is totally bogus because it results from an erroneous cancelling of pounds-force (of thrust) by pounds-mass (of propellant). In SI, the name number represents specific impulse in either m/sec or N-s/kg, both having far more intuitive meanings than "seconds".
With SI, entirely different unit names are used for mass (kilogram) and force (newton) so there's no chance for confusion. Except for those misguided souls who put "kilograms force" on torque wrenches...
Re: The "DPS should have dug a blast crater" Meme « Reply #66 on Feb 21, 2012, 8:47pm »
But the EES unit of mass is the slug, not the pound. Saying "pounds-mass" is as wrong in rigorous engineering as it is to say "kilograms-force." In each system, in the appropriate computations, we use the constant g0 to refer to the conversion between mass and Earth gravity force units, where appropriate. This is the constant that allows us to use the same units for specific impulse whether we're working in EES or SI.
The cheapness of Bob's solution is its reward. I highly doubt anyone wants to pay $32,000 for my refinement using best methods. Bob gave you a defensible answer for free.
Absolutely correct, of course, but far too subtle for the deniers. Besides the general innumeracy characteristic of pseudoscience of all kinds, the whole notion of a loose upper or lower bound based on a simplified model seems utterly alien to them.
They can't understand how anything but an exact model can possibly mean anything, nor do they accept the fact that we engineers do this sort of thing all the time. So often that we have an expression for it: a "back of the envelope" calculation.
But the EES unit of mass is the slug, not the pound.
Correct, but who the hell knows what a 'slug' is?
I know now, but I sure didn't when I first encountered it. My high school physics teacher was a SI evangelist; I think that's where I get it from. So it was a shock to get to college and find the mechanical engineering professors (who weren't even American) did everything in traditional units. And what the hell was a 'slug', anyway? Rather than remember all the stupid constants that I'd frequently forget because I was accustomed to working in SI, I converted everything to SI, did the calculations and converted the answers back to traditional.
Quote:
Saying "pounds-mass" is as wrong in rigorous engineering as it is to say "kilograms-force."
True, but done very often because even engineers have a better feeling for mass in pounds than in slugs.
Quote:
In each system, in the appropriate computations, we use the constant g0 to refer to the conversion between mass and Earth gravity force units, where appropriate. This is the constant that allows us to use the same units for specific impulse whether we're working in EES or SI.
Yes, but it's offensive. Why should I have to introduce a physical property of the planet Earth into a calculation regarding the performance of a rocket engine that might even be in deep space somewhere?
I wouldn't expect a layman to know what a slug is, but I learned back in high school and it became a familiar and commonly used term after that. I hadn't even heard of the term pound-mass until about 15 years ago. Prior to that, pounds were "weight" and it was understood that weight had to be converted to the only proper unit of mass in the fps system, the slug, by dividing by go.
Re: The "DPS should have dug a blast crater" Meme « Reply #70 on Feb 22, 2012, 2:04am »
Well, thanks to my high school physics teacher (who was actually quite good) we never even learned what a 'slug' was. We did everything in SI and he'd take nothing else. This was in the early 1970s, and of course the United States would be completely metric/SI in just a few years so why bother learning obsolete stuff?
This was in the early 1970s, and of course the United States would be completely metric/SI in just a few years so why bother learning obsolete stuff?
Even if he'd been right about the US going metric, he'd still be wrong about ignoring the Imperial units, because obsolete and obsolescent are not the same. The UK engineering industry switched to SI units four decades back, but there are still products around that pre-date the switch, so I had to be able to work in both systems throughout my career.
Joined: May 2005 Gender: Male Posts: 254 Location: Denham, England
Re: The "DPS should have dug a blast crater" Meme « Reply #72 on Feb 22, 2012, 8:21am »
Even Tesco have gone SI. They did a while back to much fanfare. I wish we'd bite the bullet and change our roads too. At least try it out in Northern Ireland since the Republic went ages ago. The problem is the political connotations from you-know-what. If it hadn't been for the incident with the grocer we'd be much further done the road.
I have mixed feelings on aviation units. It is stupid visibility is reported is metres while distance is measured in nautical miles. Also runway declared lengths are in metres. Switching to km for distance shouldn't be too stressful. It's heights that concern me. Thousands of feet is just such a convenient denomination physically. I'd be inclined to stick with feet there and metricate the rest.
Oil industry eesh! It would be a start if we could get consistent with ourselves, for example not measuring bottom hole pressure in psi and wellhead pressure in bar. That kind of thing can and has killed people. Or how about the way some teams will measure well depths in metres and others in feet. As if keeping a consistent datum and being clear whether the depth in measured or true vertical wasn't enough peril.
Well, thanks to my high school physics teacher (who was actually quite good) we never even learned what a 'slug' was. We did everything in SI and he'd take nothing else. This was in the early 1970s, and of course the United States would be completely metric/SI in just a few years so why bother learning obsolete stuff?
I don't remember high school well enough to comment, but in college we regularly used both systems of units (late 70s). I remember the exercises in my texts books frequently alternated between systems, with one problem in fps and the next in mks. We became fluent in both systems, so it's never been a source of confusion for me. I often find it frustrating when people don't understand units because I consider it so fundamental.
Yes, but it's offensive. Why should I have to introduce a physical property of the planet Earth into a calculation regarding the performance of a rocket engine that might even be in deep space somewhere?
I don't have a problem with that since go is embedded in the units. By definition,
1 Newton = 1 kilogram X go 1 pound = 1 slug X go
(EDIT) Sorry, the above is incorrect. See posts #78 and 79 for correction and retraction.
1 Newton = 1 kilogram X 1 m/s2 1 pound = 1 slug X 1 ft/s2
True, but done very often because even engineers have a better feeling for mass in pounds than in slugs.
It's true that engineers have a better feel for pounds-mass, but when solving problems I'd much rather convert to slugs and work in the proper units.
One of the most frustrating things I encountered when I first started studying rocketry was that most of the equations I found in American literature were written so that mass was entered in units of pound-mass. That is, they included go in the equations as a conversion factor. The equations wouldn't work as written using mks units unless one used kilograms-force instead of Newtons. I thought is was a bunch of BS that the equations were written to use what I consider phony units. When I wrote my web page I stripped the conversion factor out of the equations and mandated that only correct units be used, that is, Newtons-kilograms and pounds-slugs. (If people don't understand the correct units then they need to school themselves and figure it out.)
The only place that I actually added go was to the equation for specific impulse, which I write Isp=F/qgo. I did this because of the common convention of expressing Isp in units of seconds, which I actually prefer because it gives the same recognizable number irrespective of the system of units. What people need to recognize is that the calculation lbf/(lbm/s) or kgf/(kgm/s) is the same thing as lbf/(slug/s*go) or N/(kg/s*go). My equation is the only way to write it if one insists on using proper units and if one wants an answer is seconds.
Re: The "DPS should have dug a blast crater" Meme « Reply #74 on Feb 22, 2012, 1:08pm »
A comparison of bulking values of various substances revealed a material that is very similar in bulking value, similar in particle size and similar in particle distribution to lunar regolith.
lunar regolith 0.22 gms / cm3 (on Moon) powdered milk 0.21 gms / cm3 (on Earth)
lunar regolith 1.5 gms / cm3 (on Earth)(average) portland cement 1.5 gms / cm3 (on earth)
The concept of mass on Earth is the same unit of mass anywhere, on one level makes sense. But what the posted equations do not take into account is weight or gravity difference.
For instance if we landed a descent rocket engine on Earth would you have to use 15,864 pounds of thrust and use portand cement to simulate 1.5 gms / cm3 regolith, for landing on the moon or could you adjust the thrust and the regolith density using 2,644 pounds of thrust and powdered milk at .22 gms / cm3 as the regolith substitute?
The weight and feel of the regolith on the moon for all practical proposes would be similar to the weight and feel of powdered milk on earth.
How is the weight (gravity) difference accounted for? I must be missing something basic!
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