Joined: May 2005 Gender: Male Posts: 3,072 Location: Dayton, Ohio
Re: The "DPS should have dug a blast crater" Meme « Reply #75 on Feb 22, 2012, 1:33pm »
The weight of the soil on the Moon is less than on Earth, but not it's mass. The problem we are solving involves kinetic energy, which is equal to 1/2 x mass x velocity2. Weight has nothing to do with it. The kinetic energy equation allows us to calculate the mass of material moved. To convert that to a volume we divide by the mass density. The mass density of a substance is unaffected by gravity - it is the same on both Earth and the moon.
How is the weight (gravity) difference accounted for? I must be missing something basic!
Gravity plays a role if we were dealing with forces and accelerations, but we're not; we're dealing with energy. For instance, if we wanted to determine the velocity a soil particle will attain we would need to analyze all the forces acting on it. One of those forces is gravity and we must account for it. However, in the problem we're discussing, we already know how fast the particle is moving. All those forces are irrelevant now. We just want to know how much mass is required to produce a known amount of kinetic energy at a known velocity. Once we know the mass, we calculate the volume by dividing by the mass density. Gravity is irrelevant.
(edit) On the other hand, in the case of the LM, we are dealing with forces and accelerations. In that case we must take gravity into consideration, which we do by calculating the LM's weight in lunar gravity and counteracting it by using an upward thrust (force) equal to the weight.
Re: The "DPS should have dug a blast crater" Meme « Reply #77 on Feb 22, 2012, 2:25pm »
A 179 pound ball on earth takes 6 times more energy to move then a 179 pound (29.8 adjusted for gravity) ball on the moon. How can this correlate to problem of kinetic energy transfer on the Moon vs on the Earth? The mass may be the same but the weight of the mass is not. Is kenetic energy transfer equations of any realistic value or should we be looking at another method to determine the effect of exhaust on regolith?
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
No, that's just my point!
1 Newton = 1 kilogram x 1 m/sec2, or the force required to accelerate a mass of 1 kg by 1 m/sec2.
So the earth's acceleration of gravity, g0, can be given as approximately either 9.8 m/s2 or as 9.8 N/kg. (I would teach it both ways, as both have obvious physical meaning.) So g0 does not show up in SI unless you're actually discussing earth's gravity, or accelerations normalized to earth's gravity.
I think your second formula is incorrect also. 1 pound-force is the force that accelerates 1 slug of mass at a rate of 1 ft/sec2.
Re: The "DPS should have dug a blast crater" Meme « Reply #80 on Feb 22, 2012, 2:39pm »
I just discovered while checking this stuff at Wikipedia that there actually was (is?) an attempt to screw up SI in the exact same way that the English system is screwed up, by confusing mass with force and then introducing another unit of mass to "fix" it that's tied to the gravitational properties of the earth. This is the hyl or "metric slug" (neither of which I'd ever heard of before). It's 9.8 kg, the SI mass that accelerates at 1 m/s2 under a force of 1 kg-f.
I had heard of the pond and kilopond, though infrequently, as synonyms for 1 gram-force and 1 kilogram-force. But still...ah hem....
Oh crap! You're right. What was I thinking. Momentary brain freeze.
This is exactly why good old Mr. George Roemer at Dulaney Senior High only let us use metric units. And he would as frequently say "kilogram meter per second squared" as "Newton" to ensure that we understand their equivalence. Hence, no momentary brain freeze just now. See what I mean?
A 179 pound ball on earth takes 6 times more energy to move then a 179 pound (29.8 adjusted for gravity) ball on the moon.
No.
If you want to lift the ball, then yes it takes more force to do so. Why? Because lifting incorporates more than just moving the ball; it requires opposing and overcoming another force that's trying to move the ball toward the center of the planet.
Moving the ball sideways isn't overcoming the force of gravity. It's only overcoming the inertia of the ball, and inertia is a product solely of mass. The problem of moving soil laterally across the surface -- i.e., entraining it in an exhaust flow -- is an inertia problem, not a force-of-gravity problem.
Oh crap! You're right. What was I thinking. Momentary brain freeze.
This is exactly why good old Mr. George Roemer at Dulaney Senior High only let us use metric units. And he would as frequently say "kilogram meter per second squared" as "Newton" to ensure that we understand their equivalence. Hence, no momentary brain freeze just now. See what I mean?
I really don't see what you mean because the mistake I made had nothing to do with two systems of units. I would have made the same mistake if I had only been using metric units.
Re: The "DPS should have dug a blast crater" Meme « Reply #86 on Feb 22, 2012, 3:07pm »
I understand what you are saying concerning energy transfer. These equations predict 100% transfer of energy at maximum velocity, which does not seem realistic or possible, there would be a variation in acceleration of particles < 1,000 m & >1,000 m / sec.
To be of any practical relevance in demonstrating the lack of a crater it must be demonstrated how 2,644 pounds of thrust will have a negligible effect on an area with lunar regolith that has the effective weight of powdered milk. Someone blowing 5 times into powdered milk will create a deeper crater then is being predicted with a lunar lander.
A 179 pound ball on earth takes 6 times more energy to move then a 179 pound (29.8 adjusted for gravity) ball on the moon.
As Jay pointed out, it only takes more energy if you are lifting the ball. Let's say we lift the ball 5 feet. At the higher elevation the ball possesses greater potential energy; we therefore have to add energy to the ball to lift it. The amount of energy added to the same ball is 6 times greater at the surface of Earth than at the surface of the moon.
However, the problem we've been dealing with involves kinetic energy, i.e. the energy of motion. A 179 pound-mass ball moving at, say 10 ft/s, has the same kinetic energy on Earth as it does on the moon.
To be of any practical relevance in demonstrating the lack of a crater it must be demonstrated how 2,644 pounds of thrust will have a negligible effect on an area with lunar regolith that has the effective weight of powdered milk. Someone blowing 5 times into powdered milk will create a deeper crater then is being predicted with a lunar lander.
When you blow into a substance it's not flying away at 1000+ m/s.
You're making the same mistake that a lot of other people make. You seem to believe that adding a large amount of energy to the soil must mean that a large volume of soil is transported away. That is not the necessary requirement. Adding a large amount of energy to the soil can also mean that a small volume of soil is transported away at a very high velocity. Kinetic energy is mv2/2, so a small mass of material at high velocity can have the same kinetic energy as a large mass at low velocity. We know from observation that the soil flew away at very high velocity, so we should expect the volume of material to be small rather than large.
We know the kinetic energy in the exhaust with good confidence. We also know the amount of energy transferred to the soil can be no greater than the amount of energy that's in the exhaust. We also know the estimated velocity of the soil. Given these known values, it is straight forward math to estimate the mass of soil blown away by the exhaust. This has already been done and the answer tells us that a large crater will not form.
Re: The "DPS should have dug a blast crater" Meme « Reply #89 on Feb 22, 2012, 4:42pm »
A lot of engineering still occurs on Earth rather than in space or on other planets, and so a lot of practical engineering still involves dealing with the force of Earth gravity on some sort of mass. This is what continues to motivate a "simple" system of units that requires few arbitrary conversions.
The metric-speaking world still weighs things in kilograms. The imperial-speaking world still weighs things in pounds. This is because our knee-jerk reaction is always still to determine mass by measuring the force of Earth gravity on it. The casual users of both systems just happened to have fallen on different sides of the fence about which unit to use as the practical measure for non-engineering purposes.
But each tradition has created a consistent subset of units that serves formal engineering. One engineers in SI, not metric. One also engineers in EES, not imperial. The flaw in both approaches comes from reusing familiar quantities and concepts from the looser parent systems. Someone who weighs himself in the bathroom at 51 kg that morning and goes to work as an engineer dealing with forces in newtons is going to have just as much mental anguish as the person who weighs himself at 112 lbs and then has to go to his own engineering office and reckon the mass of a beam in slugs.
Once you realize that all the units involved are arbitrary, regardless of the system, and that the problems we face come not from the beauty or clunkiness of the system but from the inherent inconsistency in the problems we want to solve, the advocacy of one system over another becomes distractive. Yes, standardization is a good goal. But as long as our intuitive notion of mass is so inexorably connected to our planet's gravity, we'll have this problem.
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