Okay, but how does this permit (require?) a FASTER acceleration in the first minute? It almost makes sense intuitively somehow, but I’d love to hear a straightforward engineering/physics explanation.
Start with: F = m * a
In the case of leaving the surface of a planet:
Acceleration away from surface = (thrust / mass) - (gravitational acceleration)
Comparing the Moon launch to the Earth launch, gravitational acceleration is one-sixth and mass is dramatically lower, both of which tend to yield a better net acceleration.
The single biggest contribution to the apparent difference in launch speed is optical. The Saturn V was 363 feet tall. The LEM ascent stage about 9. It takes the Saturn V 40 times as long to travel it’s own length than the LM travelling at the same speed.
Accelerations were limited by the maximum stress you could apply to the structure and the crew. Once the fuel load decreased it was necessary to throttle back the Saturn (partly by shutting down the centre engine). The LEM ascent motor didn’t throttle. Again part of it total simplicity.
That said, the Saturn V did start slower. Thrust of about 7,600,000 pounds, all up mass at launch 6,300,000 pounds. Leaving you with 1,300,000 pounds of thrust after the gravitational weight is subtracted, and a take off acceleration of about 2.5m/s[sup]2[/sup] Compare to the LEM ascent stage, thrust of 3,500 pounds, all up mass 10,000 pounds, but in lunar gravity a gravitational weight of only 1,700 pounds. So the initial acceleration was more like 4m/s[sup]2[/sup]. Greater, but nothing like as much as you would think from the video.
Just the usual nitpick. Mass was identical. The force due to gravity was one sixth. I have termed this the gravitational weight above, which is pedantically correct (if sometimes confusing.)
Darn it. I got the subtraction backwards. The initial acceleration of the LEM was less than the Saturn V. 1.8m/s[sup]2[/sup] versus 2.5m/s[sup]2[/sup].
So all down to the absolute sizes making the difference in apparent rate.
Really? You just told us it was 0.016% of the initial mass when leaving the Earth.
Ah, mea culpa. I misread the sentence. I though you had made the usual weight versus mass mistake. :smack:
The LEM ascent had far less mass to move than the Saturn 5 liftoff. Much less mass under 1/6th gravity means far less force needed to boost.
As already mentioned by Francis Vaughn the propellants on the Saturn S-I stage were LOX and RP-1 (liquid oxygen and high grade kerosene). The products of this combustion create a greyish-brown exhaust cloud. However, the large volume of vapor you see is water, albeit that produced by vaporizing water that is in the flame trench below the launch stand. This is done to attenuate the acoustic random vibration environment that is reflected from the plume.
The Shuttle Solid Rocket Booster (SRB) propellant formaulation changed slightly over the years, but it was essentially a cast composite propellant, of a formulation known as TP-H1148 (“TP” stands for Thiokol Propellant) which consisted of 16% propellant-grade powdered aluminum as the fuel, 69.6% amonium perchlorate, 0.4% iron oxide as a burn rate modifier, 12% polybutadine acrylic acid acrylonitrile terpolymer (PBAN) as a propellant binder, and ~2% Thiokol proprietary curing agent. (Despite the fact that the SRBs are derived by ignornant people as “sticks of dynamite strapped to the Shuttle”, this formulation does not contain any high explosive agents such as HMX or RDX that are often added to high performance propellant formulations and has always been classifiied as a Hazard Class 1.3d substance.) The exhaust of the Al and NH[SUB]4[/SUB]ClO[SUB]4[/SUB] produces a thick white cloud, but the PBAN and iron produce the dirtier products.
The same propellants were used in the Titan II and subsequent Titan-family systems, and were also used in the vaunded Soviet SS-18 heavy lift ICBM (which is currently in use as a satellite launch vehicle), albeit in much larger pump-fed engines. These propellants have some very nice properties in addition to being storable; they are highly energetic, hypergolic (self-igniting), and sufficiently dense that the high molecular weight of the products (which translates into lower exhaust velocities, and therefore lower propulsive efficiency) is offset by the fact that it is easier to push a lot of mass through the nozzle than LH/LOX or even RP-1/LOX. Unfortunately, the propellants are also highly reactive, extremely toxic (as is the exhaust), and very expensive, and so are no longer in use except for reaction control systems and small upper stage engines. The main point of the design, however, was to ensure utter reliability under variable environment conditions and the ability to restart, which led to the pressure feed system and pintle injector. BTW, the Merlin engines used on the Falcon 1 and Falcon 9 rockets are a direct descentant of this engine through a series of developments by Grumman and TRW (now Northrop Grumman). The design was literally copied, with minor modifications, on an earlier TRW-developed low cost liquid booster vehicle that was intended to be part of an EELV-type family that was not selected.
To be fair, the Saturn V had three stages with multiple engines apiece to status and ready, in addition to the manned capsule and complex guidance system. The LM had a single engine and a guidance system less powerful than the cell phone you disposed of ten years ago.
The thrust-to-weight ratio–that is, the amount of lifting force developed versus the weight of the vehicle–is substantially different, both due to the 500% difference in weight between the surface of the Moon and that of the Earth, and the amount of dead weight that has to be carried by the LM and the Saturn V. The LM carried the engine, propellants, and a very small habitat capsule, while the Saturn V carried two large upper stages, the LM, the Command/Service Module, and (in J class missions) the Lunar Rover Vehicle, plus a bunch of avionics and other instruments. The Saturn V at maximum payload is actually too heavy to lift off for the first few seconds of S-IC action. This is intentional, as it allows time for the stage to build full thrust and perform a live vehicle systems check before actual liftoff, something that the Shuttle could not do after SRB ignitition. (STS actually ignited the main engines slightly before SRB so they could be checked, and positive function was verified before SRB ignition, allowing an on-pad abort up to that point.) Plans for a heavy(ier) lift version of the Saturn V involved the use of 4, 6, or 8 large strap-on solids, but there is some question that this would have really been viable without completely redesigning the Saturn V. Anyway, the Saturn V actually has to burn off some propellant while building up to full thrust before it can move, whereas the LM ascent stage has overunity thrust as soon as the ignition transient clears the nozzle, and therefore scoots much faster. The same is true for most purely solid propellant vehicles such as ICBMs like the LGM-118A ‘Peacekeeper’, and especaily SLBMs like the Trident family, both of which are boosted up into the air before igntion, and have to recover and go before they fall back down.
The real concern about atmosphere isn’t at liftoff (except for the temperature and acoustic environment it creates) but at a point called max-Q alpha, which is aerodynamics-sprechen for “the point of maximum aerodynamic loading”. This is usually just at or above the speed of sound, generally occurring at less than 60kft (it depends on the speed, aerodynamic shape, and angle of attack) and is the limiting structural case for most space launch vehicles, requiring them to throttle down. The LM ascent stage, of course, doesn’t fly in atmosphere and therefore has no worries about max-Q alpha.
Stranger
The orbital speed of the command module was something like 1600 mph. That’s less than half the max. speed of a WWII V-2 rocket. So it doesn’t take a big rocket to get the ascent stage up to that speed. (And once off the surface, they used very small impulse rockets to change orbits.)
Thank you all! I actually thought of the optical effect of a long vehicle just after I posted, and figured someone would mention it as at least part of the answer.