Monthly Archives: August 2015

my electric cart of the future

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Buxbaum and Sperka cart of future

Buxbaum and Sperka show off the (shopping) cart of future, Oak Park parade July 4, 2015.

A Roman chariot did quite well with only 1 horse-power, while the average US car requires 100 horses. Part of the problem is that our cars weigh more than a chariot and go faster, 80 mph vs of 25 mph. But most city applications don’t need all that weight nor all of that speed. 20-25 mph is fine for round-town errands, and should be particularly suited to use by young drivers and seniors.

To show what can be done with a light vehicle that only has to go 20 mph, I made this modified shopping cart, and fitted it with a small, 1 hp motor. I call it the cart-of the future and paraded around with it at our last 4th of July parade. It’s high off the ground for safety, reasonably wide for stability, and has the shopping cart cage and seat-belts for safety. There is also speed control. We went pretty slow in the parade, but here’s a link to a video of the cart zipping down the street at 17.5 mph.

In the 2 months since this picture was taken, I’ve modified the cart to have a chain drive and a rear-wheel differential — helpful for turning. My next modification, if I get to it, will be to switch to hydrogen power via a fuel cell. One of the main products we make is hydrogen generators, and I’m hoping to use the cart to advertise the advantages of hydrogen power.

Robert E. Buxbaum, August 28, 2015. I’m the one in the beige suit.

Racial symbols: OK or racist

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Washington Redskins logo and symbol. Shows race or racism?

Washington Redskins lost protection of their logo and indian symbol. Symbol of race or racism?

In law, one generally strives for uniformity, as in Leviticus 24:22: “You shall have one manner of law; the same for the home-born as for the stranger,”  but there are problems with putting this into effect when dealing with racism. The law seems to allow each individual group to denigrate itself with words that outsiders are not permitted. This is seen regularly in rap songs but also in advertising.

Roughly a year ago, the US Patent office revoked the copyright protection for the Washington Redskin logo and for the team name causing large financial loss to the Redskins organization. The patent office cited this symbol as the most racist-offensive in sports. I suspect this is bad law, in part because it appears non-uniform, and in part because I’m fairly sure it isn’t the most racist-offensive name or symbol. To pick to punish this team seems (to me) an arbitrary, capricious use of power. I’ll assume there are some who are bothered by the name Redskin, but suspect there are others who take pride in the name and symbol. The image is of a strong, healthy individual, as befits a sports team. If some are offended, is his (or her) opinion enough to deprive the team of its merchandise copyright, and to deprive those who approve?

More racist, in my opinion, is the fighting Irishman of Notre Dame. He looks thick-headed, unfit, and not particularly bright: more like a Leprechaun than a human being. As for offensive, he seems to fit a racial stereotype that Irishmen get drunk and get into fights. Yet the US Patent office protects him for the organization, but not the Washington Redskin. Doesn’t the 14th amendment guarantee “equal protection of the laws;” why does Notre Dame get unequal protection?

Notre Damme Fighting Irish. Is this an offensive stereotype.

Notre Dame’s Fighting Irishman is still a protected symbol. Is he a less-offensive, racist stereotype?

Perhaps what protects the Notre Dame Irishman is that he’s a white man, and we worry more about insulting brown people than white ones. But this too seems unequal: a sort of reverse discrimination. And I’m not sure the protection of the 14th was meant to extend to feelings this way. In either case, I note there are many other indian-named sports teams, e.g. the Indians, Braves, and Chiefs, and some of their mascots seem worse: the Cleveland Indians’ mascot, “Chief Wahoo,” for example.

Chief Wahoo, symbol of the Cleveland Indians. Still protected logo --looks more racist than the Redskin to me.

Chief Wahoo, Still protected symbol of the Cleveland Indians –looks more racist than the Redskin to me.

And then there’s the problem of figuring out how racist is too racist. I’m told that Canadians find the words Indian and Eskimo offensive, and have banned these words in all official forms. I imagine some Americans find them racist too, but we have not. To me it seems that an insult-based law must include a clear standard of  how insulting the racist comment has to be. If there is no standard, there should be no law. In the US, there is a hockey team called the Escanaba (Michigan) Eskimos; their name is protected. There is also an ice-cream sandwich called Eskimo Pie — with an Eskimo on the label. Are these protected because there are relatively fewer Eskimos or because eskimos are assumed to be less-easily insulted? All this seems like an arbitrary distinction, and thus a violation of the “equal protection” clause.

And is no weight given if some people take pride in the symbol: should their pride be allowed balance the offense taken by others? Yankee, originally an insulting term for a colonial New Englander became a sign of pride in the American Revolution. Similarly, Knickerbocker was once an insulting term for a Dutch New Yorker; I don’t think there are many Dutch who are still insulted, but if a few are, can we allow the non-insulted to balance them. Then there’s “The Canucks”, an offensive term for Canadian, and the Boston Celtic, a stereotypical Irishman, but also a mark of pride of how far the Irish have come in Boston society. Tar-heel and Hoosiers are regional terms for white trash, but now accepted. There must be some standard of insult here, but I see none.

The Frito Bandito, ambassador of Frito Lays corn chips.

The Frito Bandito, ambassador of Frito Lays corn chips; still protected, but looks racist to me.

Somehow, things seem to get more acceptable, not less if the racial slur is over the top. This is the case, I guess with the Frito Bandito — as insulting a Mexican as I can imagine, actually worse than Chief Wahoo. I’d think that the law should not allow for an arbitrary distinction like this. What sort of normal person objects to the handsome Redskin Indian, but not to Wahoo or the Bandito? And where does Uncle Ben fit in? The symbol of uncle Ben’s rice appears to me as a handsome, older black man dressed as a high-end waiter. This seems respectable, but I can imagine someone seeing an “uncle tom,” or being insulted that a black man is a waiter. Is this enough offense  to upend the company? Upending a company over that would seem to offend all other waiters: is their job so disgusting that no black man can ever be depicted doing it? I’m not a lawyer or a preacher, but it seems to me that promoting the higher levels of respect and civil society is the job of preachers not of the law. I imagine it’s the job of the law to protect contracts, life, and property. As such the law should be clear, uniform and simple. I can imagine the law removing a symbol to prevent a riot, or to maintain intellectual property rights (e.g. keeping the Atlanta Brave from looking too much like the Cleveland Indian). But I’d think to give people wide berth to choose their brand expression. Still, what do I know?

Robert Buxbaum, August 26, 2015. I hold 12 patents, mostly in hydrogen, and have at least one more pending. I hope they are not revoked on the basis that someone is offended. I’ve also blogged a racist joke about Canadians, and about an Italian funeral.

Winning at Bunker Hill lost America for Britain.

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The greatest single victory of the American Revolution in terms of British soldiers killed or wounded was the battle of Bunker Hill. It was won without global strategy, or any real sense of victory. Though the British held the hill when the battle was over, the loss of soldiers and reputation, was such that one can easily echo the comment of British General, George Clinton: “A few more such victories would have shortly put an end to British dominion in America.” How the British came to blunder this way is a real lesson in group-think leading to the destruction of an army of the finest soldiers on earth, made more humiliating because it was destroyed by a band of untrained, leader-less rabble.

By May 1775, Boston was already a major colonial port. British-controlled, but much smaller than it is today, it consisted of a knob-hill peninsula cut off from the rest of the colonies except for one narrow road, called “The Neck,” or The Roxbury Neck. The later name was used to distinguish it from a similar neck road leading that connected the colonies to nearby Charlestown peninsula (Bunker Hill is on Charlestown peninsula). Following the rumpus battles of Lexington and Concord, Boston was surrounded by 15,000 ill-clad, undisciplined colonials who ate, drank, and shot at stuff in plain view of the 6000 trained soldiers and 4 Generals quartered in Boston. The Colonials had set up barriers and cannon at their end of the Neck road. The British army could still leave by that route to demonstrate control of the colonies, but only at a cost — one that kept rising as more colonials came to camp out around Boston.

The British had sea-power though, excellent ships and excellent admirals; the colonies had neither. The British could their navy it to attack anywhere on the American coast, but only at a risk or alienating the colonials. They thus used the sea power judicially. For their attack on Lexington, April ’75, they used ships to take 2000 soldiers from Boston for a naval landing at Charlestown, at the foot of Breed’s hill. The army then marched out over the Charlestown neck towards Lexington. The battle was not a smashing success. Back in Boston, the four British generals: Gage, Burgoyne, Howe, and Clinton, realized that, to quash the revolt/revolution, they had to break out permanently from the Boston peninsula and quarter in Massachusetts proper. They needed to take and hold some easily defended ground on the mainland, preferably high ground. They needed to establish a base with good connections to the rest of coast, and good access to the sea. Looking about Boston, the obvious spot for this base was the heights of Dorchester, a set of hills that overlooked Boston Harbor from the south. Eventually George Washington captured and held these heights causing the British to flee. The heights were undefended because, by incredible ignorance, on the morning of June 17 the British changed their goals, and decided to attack at Charlestown (Breed’s Hill), and not at Dorchester. The victory at Charlestown left Britain with many dead and no good connection to the colonies, just another isolated peninsula barely attached to the mainland by an easily defended road.

What caused four trained Generals to attack at this worthless spot was American disarray: the advantage of America’s mob-rule against British group-think. Each British General saw an opportunity for personal glory at this worthless target – the same group-think that would happen in the Crimean war. Too many cooks spoil the broth, etc. The British decided to attack at Charlestown because the confusion of the American meant that the defense of the city and of Breeds Hill was done incredibly poorly. A poor location was chosen for a fort and only 1200 Colonials came to defend it. We’d meant to build a fort at Bunker Hill, a tall hill overlooking Boston, and we’d meant to build a secondary foxhole on Breeds hill. Digging  at night with much rum and confused leadership (or no leadership), we found, when the sun rose, that we’d built next to nothing on Bunker hill, and a vastly too-large, too deep, square hole or trench at Breed’s Hill: a doubtful redoubt. The trench was open at back, too large for the number of soldiers, and too deep for people to shoot out of easily. Looking with spyglasses from Boston, the British could see that the Continentals had no idea what they were doing, and Gage thought to show them the consequences. British soldiers could easily take this redoubt and the 1200 defenders, and that thought clouded his mind and the minds of his co-generals to the bigger issue: this was not a hill worth taking. Even if the British could win without a single loss, they’d be in a worse position for breaking out of Boston. Even if there were no loosed, the British forces would be divided between two peninsulas separated from the mainland by two neck-roads. Coordinating an attack would be a logistic nightmare, and any one of the Generals should have seen that.

The attack was supposed to work this way: a sea landing at Moulton's hill. two side actions, SA, at the fronts of the Colonial defenses, and a sweeping main attack, MA, at the edge.

The attack was supposed to work this way: a sea landing at Moulton’s hill. two side actions, SA, at the fronts of the Colonial defenses, and a sweeping main attack, MA, at the edge.

But four generals working together were stupider than one would have been. Any one could have remembered why Dorchester Heights was the right military goal, as originally planned. But the group think of four generals, each more gleeful than his fellow at the incompetence of the rebels made attacking there too tempting to ignore. If they could get a superior force of trained men to land at Charlestown, they could have them march forward to an easy victory and personal glory. Against this rabble they might even do it with bayonets alone. The Continentals had too few men, no training, and no bayonets. If the Continentals were able to muster together at all (unlikely), they were unlikely to be able to reload fast or shoot fast — that took special guns and training. The colonials would likely miss with half their shots and then fumble. The British would arrive at the trench before the Continentals could reload. The superior British force could shoot rebels at close range or spear them with their bayonets. There was a small problem the British saw: the Americans had bought a cannon to the hill, and a trained cannoneer could fire grape-shot. They thus decided on a complex attack with a feint to the front and a side run. What they didn’t know was that the Americans had little powder and no idea what to do with the cannon. The British plan was to form a single line, fake an attack at redoubt staying out of range of the grape shot, and then wheel right. That is every British soldier in the line was to turn right and march north to the trench’s right side (the left side if you look as a Colonial). They’d avoid the cannon and take the redoubt from the side. It should have been a piece of cake.

Unfortunately landing the troops and forming them up took longer than expected, and this allowed more Colonials to show up and fix some of the more-glaring errors of their defense. The British discovered they had trouble mustering into an appropriate line for attack because colonials positioned themselves in Charlestown and took potshots at the officers. Meanwhile, the Continentals build up the left side of their redoubt (the side the British wished to attack). The colonials built triangular sub forts (Friches) at both sides of the trench, somewhat in front, and built a rail fence-from the hill to the sea on the left (north) side somewhat behind. The British naval commander wasted yet more time with a cannon barrage from his ships in the harbor. The barrage managed to kill only one colonial, decapitated by a cannon-ball, while the colonials built more defenses and did more sniper shooting. Col. Stark of the colonials put up shot markers at 100 feet from the fence and passed the now-famous instruction: don’t shoot till you see the whites of their eyes. The assumption is that, at 50 to 100 feet, colonial shooters would not miss while any British who passed the fence would be taken out by the defenders on Bunker Hill.

The second attack at Breeds Hill

The second attack at Breeds Hill

At first the British tried the two frontal attacks described above with a wheel to the north. But this attack failed; it was too complicated. The front line was composed of crack Hessians who marched perfectly in step, but they were wearing their bright red coats and with heavy bear-skin hats (Busby hats) to make them look more formidable. The ground was uneven and mucky, though, and the tall hats kept them from looking down at the brambles and rocks. The result was they moves so slowly that the colonials had time to fire once and reload. The cannon was never used, but those Hessians who survived the first shots never managed to wheel. Meanwhile, the main attack at the rail fence failed because a colonial fired early by mistake. The British force (bigger mistake) stopped and fired back, more or less in range. Hearing the shooting, more Colonials showed up and shot British soldiers using the fence to steady their aim. A few British got past the fence and got shot by retreating Americans and by the garrison on Bunker Hill. The rest were called back, allowing the British to re-muster, and allowing the Americans to reload and reposition.

The second British attack used a simpler arrangement, see map above. Three ranks of soldiers where mustered to march straight towards the fort while the generals burnt Charlestown as a way of stopping the snipers (see painting below). But the Colonials rearranged themselves. More colonials wandered onto the peninsula, and built a quick platform in the redoubt so they could shoot better over the top. Some defenders of Bunker Hill — folks who’d seen little action so far — moved forward to defend the fence, and some Colonial soldiers wandered off, too. The British attacked without  trying to wheel, and the result was many British dead or wounded. The attack was called off.

The second attack: Three ranks and no Busby hats this time, with Charlestown burning in the background. Their's not to question why, their's but to do and die.

The second attack: Three ranks and no Busby hats this time, with the dead strewn around and Charlestown burning in the background. Their’s not to question why; their’s but to do and die. Painting by Pyle.

Eventually, the British organized their men for a third attack, adding some 400 marines (ship-board soldiers) plus some 200 wounded who were ordered to re-muster. This attack would be even simpler than the last. The men were arranged in columns, not rows, and sent straight up to the front of the fort. The folks in front were killed, but the attack worked in part because it robbed the Colonials of ammunition. While the British managed to take the fort this time, most of the defenders avoided capture. They retreated across the neck and rejoined the main mob. The British captured or killed some 400 colonials at the expense of 1,054 men lost (226 killed in the immediate battle) including most of their junior officers. The British also lost the sense of invincibility; colonials could inflict serious damage at minimal cost.

The Colonials were able to pick off British officers because they dressed better than the rest — a mistake the British would keep making. At Bunker Hill, the British lost 1 lieutenant colonel (killed), 5 majors (3 killed), 34 captains (7 killed) 41 lieutenants (9 killed), 57 sergeants (15 killed), and 13 drummers (1 killed). A lesson: don’t dress so fancy. More importantly, the British forces were now divided between two peninsulas. The men defending these peninsulas were now unavailable to attack at Dorchester heights. That is, it was a costly victory that cost the British forces the escape from Boston that they needed if they were to hold the colonies. By January 1776 the British left Boston by ship and left Charlestown peninsula as well. They would try again in 1776 and 1777, but by then the continental army would be more of an army and less of a rabble with rifles. A lesson for life: only fight for something that you really want, otherwise your win may be a loss.

After the battle, General Burgoyne blamed Generals Clinton, Howe, and Gage for the loss of men and opportunity. As a result — stung by Burgoyne’s blame — Clinton and Howe idid not come Burgoyne’s aid at Albany in June 1777. Instead, Clinton sent Howe to attack the continental congress at Philadelphia, leaving Burgoyne to defend himself, brilliant general that he claimed to be. Burgoyne lost his army and reputation, and Howe succeeded, at least a little. Philadelphia was captured, but the Continental congress fled, and Burgoyne’s defeat led to the French joining in on our side. Burgoyne was not willing to take any blame, it seems to me, because he could not see that chaos in war is far better than group-think of even the best generals.

The colonial chaos was horrible, but it was fixable. The group mistakes on the British side were not as bad, but they were impossible to fix since they evolved so much coordinated effort. Had there been fewer British generals in command, the better-trained British army would have beaten (In my opinion) a far better defense at Charlestown, or they would have ignored Charlestown and attacked a modestly defended Dorchester and won the war. General Howe beat Washington repeatedly at New York and New Jersey in the summer and fall of 1776 using the same soldiers who lost at Bunker Hill. It was only George Washington’s genius that saved some semblance of an army to keep fighting into 1777. In general, I note that the American military survives chaos and fractured leadership better than most militaries do because we are, by nature, chaotic. As Bismarck would try to explain: “God protects children, fools, and the United States of America.”

Robert Buxbaum, August 16, 2015. There were several other howler mistakes of the American Revolution. They were mostly of the same type: the British taking victories that they didn’t want, and losing opportunities that they did. One missed opportunity: they did not capture Adams and Hancock. The two fled to the Continental congress in Philadelphia where they did more mischief than they could have done in Boston. Don’t attack readily, but if you do, make sure you win.

It’s rocket science

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Here are six or so rocket science insights, some simple, some advanced. It’s a fun area of engineering that touches many areas of science and politics. Besides, some people seem to think I’m a rocket scientist.

A basic question I get asked by kids is how a rocket goes up. My answer is it does not go up. That’s mostly an illusion. The majority of the rocket — the fuel — goes down, and only the light shell goes up. People imagine they are seeing the rocket go up. Taken as a whole, fuel and shell, they both go down at 1 G: 9.8 m/s2, 32 ft/sec2.

Because 1 G ofupward acceleration is always lost to gravity, you need more thrust from the rocket engine than the weight of rocket and fuel. This can be difficult at the beginning when the rocket is heaviest. If your engine provides less thrust than the weight of your rocket, your rocket sits on the launch pad, burning. If your thrust is merely twice the weight of the rocket, you waste half of your fuel doing nothing useful, just fighting gravity. The upward acceleration you’ll see, a = F/m -1G where F is the force of the engine, and m is the mass of the rocket shell + whatever fuel is in it. 1G = 9.8m/s is the upward acceleration lost to gravity.  For model rocketry, you want to design a rocket engine so that the upward acceleration, a, is in the range 5-10 G. This range avoids wasting lots of fuel without requiring you to build the rocket too sturdy.

For NASA moon rockets, a = 0.2G approximately at liftoff increasing as fuel was used. The Saturn V rose, rather majestically, into the sky with a rocket structure that had to be only strong enough to support 1.2 times the rocket weight. Higher initial accelerations would have required more structure and bigger engines. As it was the Saturn V was the size of a skyscraper. You want the structure to be light so that the majority of weight is fuel. What makes it tricky is that the acceleration weight has to sit on an engine that gimbals (slants) and runs really hot, about 3000°C. Most engineering projects have fewer constraints than this, and are thus “not rocket science.”

Basic force balance on a rocket going up.

Basic force balance on a rocket going up.

A space rocket has to reach very high, orbital speed if the rocket is to stay up indefinitely, or nearly orbital speed for long-range, military uses. You can calculate the orbital speed by balancing the acceleration of gravity, 9.8 m/s2, against the orbital acceleration of going around the earth, a sphere of 40,000 km in circumference (that’s how the meter was defined). Orbital acceleration, a = v2/r, and r = 40,000,000 m/2π = 6,366,000m. Thus, the speed you need to stay up indefinitely is v=√(6,366,000 x 9.8) = 7900 m/s = 17,800 mph. That’s roughly Mach 35, or 35 times the speed of sound at sea level, (343 m/s). You need some altitude too, just to keep air friction from killing you, but for most missions, the main thing you need is velocity, kinetic energy, not potential energy, as I’ll show below. If your speed exceeds 17,800 m/s, you go higher up, but the stable orbital velocity is lower. The gravity force is lower higher up, and the radius to the earth higher too, but you’re balancing this lower gravity force against v2/r, so v2 has to be reduced to stay stable high up, but higher to get there. This all makes docking space-ships tricky, as I’ll explain also. Rockets are the only way practical to reach Mach 35 or anything near it. No current cannon or gun gets close.

Kinetic energy is a lot more important than potential energy for sending an object into orbit. To get a sense of the comparison, consider a one kg mass at orbital speed, 7900 m/s, and 200 km altitude. For these conditions, the kinetic energy, 1/2mv2 is 31,205 kJ, while the potential energy, mgh, is only 1,960 kJ . The potential energy is thus only 1/16 the kinetic energy.

Not that it’s easy to reach 200 miles altitude, but you can do it with a sophisticated cannon. The Germans did it with “simple”, one stage, V2-style rockets. To reach orbit, you generally need multiple stages. As a way to see this, consider that the energy content of gasoline + oxygen is about 10.5 MJ/kg (10,500 kJ/kg); this is only 1/3 of the kinetic energy of the orbital rocket, but it’s 5 times the potential energy. A fairly efficient gasoline + oxygen powered cannon could not provide orbital kinetic energy since the bullet can move no faster than the explosive vapor. In a rocket this is not a constraint since most of the mass is ejected.

A shell fired at a 45° angle that reaches 200 km altitude would go about 800 km — the distance between North Korea and Japan, or between Iran and Israel. That would require twice as much energy as a shell fired straight up, about 4000 kJ/kg. This is still within the range for a (very large) cannon or a single-stage rocket. For Russia or China to hit the US would take much more: orbital, or near orbital rocketry. To reach the moon, you need more total energy, but less kinetic energy. Moon rockets have taken the approach of first going into orbit, and only later going on. While most of the kinetic energy isn’t lost, it’s likely not the best trajectory in terms of energy use.

The force produced by a rocket is equal to the rate of mass shot out times its velocity. F = ∆(mv). To get a lot of force for each bit of fuel, you want the gas exit velocity to be as fast as possible. A typical maximum is about 2,500 m/s. Mach 10, for a gasoline – oxygen engine. The acceleration of the rocket itself is this ∆mv force divided by the total remaining mass in the rocket (rocket shell plus remaining fuel) minus 1 (gravity). Thus, if the exhaust from a rocket leaves at 2,500 m/s, and you want the rocket to accelerate upward at an average of 10 G, you must exhaust fast enough to develop 10 G, 98 m/s2. The rate of mass exhaust is the average mass of the rocket times 98/2500 = .0392/second. That is, about 3.92% of the rocket mass must be ejected each second. Assuming that the fuel for your first stage engine is less than 80% of the total mass, the first stage will flare-out in about 20 seconds. Typically, the acceleration at the end of the 20 burn is much greater than at the beginning since the rocket gets lighter as fuel is burnt. This was the case with the Apollo missions. The Saturn V started up at 0.5G but reached a maximum of 4G by the time most of the fuel was used.

If you have a good math background, you can develop a differential equation for the relation between fuel consumption and altitude or final speed. This is readily done if you know calculous, or reasonably done if you use differential methods. By either method, it turns out that, for no air friction or gravity resistance, you will reach the same speed as the exhaust when 64% of the rocket mass is exhausted. In the real world, your rocket will have to exhaust 75 or 80% of its mass as first stage fuel to reach a final speed of 2,500 m/s. This is less than 1/3 orbital speed, and reaching it requires that the rest of your rocket mass: the engine, 2nd stage, payload, and any spare fuel to handle descent (Elon Musk’s approach) must weigh less than 20-25% of the original weight of the rocket on the launch pad. This gasoline and oxygen is expensive, but not horribly so if you can reuse the rocket; that’s the motivation for NASA’s and SpaceX’s work on reusable rockets. Most orbital rocket designs require three stages to accelerate to the 7900 m/s orbital speed calculated above. The second stage is dropped from high altitude and almost invariably lost. If you can set-up and solve the differential equation above, a career in science may be for you.

Now, you might wonder about the exhaust speed I’ve been using, 2500 m/s. You’ll typically want a speed at lest this high as it’s associated with a high value of thrust-seconds per weight of fuel. Thrust seconds pre weight is called specific impulse, SI, SI = lb-seconds of thrust/lb of fuel. This approximately equals speed of exhaust (m/s) divided by 9.8 m/s2. For a high molecular weight burn it’s not easy to reach gas speed much above 2500, or values of SI much above 250, but you can get high thrust since thrust is related to momentum transfer. High thrust is why US and Russian engines typically use gasoline + oxygen. The heat of combustion of gasoline is 42 MJ/kg, but burning a kg of gasoline requires roughly 2.5 kg of oxygen. Thus, for a rocket fueled by gasoline + oxygen, the heat of combustion per kg is 42/3.5 = 12,000,000 J/kg. A typical rocket engine is 30% efficient (V2 efficiency was lower, Saturn V higher). Per corrected unit of fuel+oxygen mass, 1/2 v2 = .3 x 12,000,000; v =√7,200,000 = 2680 m/s. Adding some mass for the engine and fuel tanks, the specific impulse for this engine will be, about 250 s. This is fairly typical. Higher exhaust speeds have been achieved with hydrogen fuel, it has a higher combustion energy per weight. It is also possible to increase the engine efficiency; the Saturn V, stage 2 efficiency was nearly 50%, but the thrust was low. The sources of inefficiency include inefficiencies in compression, incomplete combustion, friction flows in the engine, and back-pressure of the atmosphere. If you can make a reliable, high efficiency engine with good lift, a career in engineering may be for you. A yet bigger challenge is doing this at a reasonable cost.

At an average acceleration of 5G = 49 m/s2 and a first stage that reaches 2500 m/s, you’ll find that the first stage burns out after 51 seconds. If the rocket were going straight up (bad idea), you’d find you are at an altitude of about 63.7 km. A better idea would be an average trajectory of 30°, leaving you at an altitude of 32 km or so. At that altitude you can expect to have far less air friction, and you can expect the second stage engine to be more efficient. It seems to me, you may want to wait another 10 seconds before firing the second stage: you’ll be 12 km higher up and it seems to me that the benefit of this will be significant. I notice that space launches wait a few seconds before firing their second stage.

As a final bit, I’d mentioned that docking a rocket with a space station is difficult, in part, because docking requires an increase in angular speed, w, but this generally goes along with a decrease in altitude; a counter-intuitive outcome. Setting the acceleration due to gravity equal to the angular acceleration, we find GM/r2 = w2r, where G is the gravitational constant, and M is the mass or the earth. Rearranging, we find that w2  = GM/r3. For high angular speed, you need small r: a low altitude. When we first went to dock a space-ship, in the early 60s, we had not realized this. When the astronauts fired the engines to dock, they found that they’d accelerate in velocity, but not in angular speed: v = wr. The faster they went, the higher up they went, but the lower the angular speed got: the fewer the orbits per day. Eventually they realized that, to dock with another ship or a space-station that is in front of you, you do not accelerate, but decelerate. When you decelerate you lose altitude and gain angular speed: you catch up with the station, but at a lower altitude. Your next step is to angle your ship near-radially to the earth, and accelerate by firing engines to the side till you dock. Like much of orbital rocketry, it’s simple, but not intuitive or easy.

Robert Buxbaum, August 12, 2015. A cannon that could reach from North Korea to Japan, say, would have to be on the order of 10 km long, running along the slope of a mountain. Even at that length, the shell would have to fire at 450 G, or so, and reach a speed about 3000 m/s, or 1/3 orbital.