There is no division by zero because it is not actual gravity. It is standard gravity (roughly sea level, 45°latitude, 9.80665 m/s or equiv in ft/s). It is purely an artifact to support lbm and lbf (and happens to be roughly the value on the surface of the earth).
I reject it too. I vaguely remember being taught how to work in gravitational units (mostly through the slug, who measures mass in slugs?), but rejected it entirely as I became more familiar with metric. Fortunately my college insisted we always work in metric. NASA will carry (standard) earth gravity to the stars and distant planets where it will clearly be NOT the nominal local gravity, but remember it is only an artifact to set unit values. If I had to compute in gravitational units, I would undoubtedly make a mistake. I would change everything to metric, solve, and change the answer back, but I have tried to force my way through these scenarios to understand what they are doing. I'm not really asserting pounds mass and pounds force are equal, but they give that appearance if you work in gravities. People who work in gravitational units have to introduce one artifact, but there are three ways of doing so yielding three forms of units for f = ma poundals (lbf x 32.17), lbm, ft/s² lbf, slugs (lbm/32.17), ft/s² lbf, lbm, gravities (ft/s² x 1/32.17) They all do the same thing, introduce standard gravity into F = ma. ________________________________ From: "mechtly, eugene a" <[email protected]> To: U.S. Metric Association <[email protected]> Cc: "mechtly, eugene a" <[email protected]> Sent: Sat, May 4, 2013 4:39:51 PM Subject: [USMA:52738] RE: NASA mT and K John (Steele), I agree with your observation that some parts of NASA are wedded to earth-gravitational ideas. How does NASA-GRC define the Specific Impulse (Isp) of a Rocket Engine operating in deep space far from earth's gravity field where the value of g and W approach zero? i.e. where W = m g and W also approaches zero? Would they still define Isp as thrust integrated over a short interval of time divided by weight (W)? or would they divide by mass, respecting CGPM resolutions and avoiding the infinity arising from division by zero? Where is the GRC "g" evaluated in W = m g? It is the NASA-GRC "definition" of Specific Impulse that I reject. The GRC equations contradict the CGPM resolution declaring the distinction between mass and weight (defined as a force). I do not agree with your assertion that mass and force are the same thing if...(under any circumstance you select)! It is true that the numerical values of mass and weight can be forced to be equal by introducing a contrived multiplication or division factor, but that *manipulation* does not make the quantities mass and force equal! Only the numerical values can be made equal in a hybrid non-system of units, e.g. where 10 lbf = 10 lbm. There are many other abuses of unit names and unit symbols in the MSFC article on Ares V and in the GRC article on Isp which deviate from standards on SI, too numerous to mention! Eugene Mechtly ________________________________ From: Kilopascal [[email protected]] Sent: Saturday, May 04, 2013 8:15 AM To: U.S. Metric Association Subject: [USMA:52737] RE: NASA mT and K They use the dreaded sec instead of s for seconds. [USMA:52737] RE: NASA mT and K John M. Steele Sat, 04 May 2013 04:59:16 -0700 I think this "derivation" of specific impulse proves NASA is fundamentally wedded to US Customary and gravitational unit systems. Metric is just a glossy conversion at the end to show EO12770 compliance. http://www.grc.nasa.gov/WWW/k-12/airplane/specimp.html At any rate, they mean burn time with the available fuel, assuming constant thrust and fuel flow, it reduces to thrust multiplied by burn time divided by fuel mass, or real specific impulse divided by earth gravity. Mass and force ARE the same thing if acceleration is divided by earth gravities. There are three ways to "fake" coherence of F = ma in Customary, poundals, slugs, or gravities. Poundals are mostly British, and most of us learned slugs in high school but NASA uses gravities. For me, learning metric was slugicide, have killed them on sight ever since.
