Power, Energy and Transportation

by ergologist@yahoo.com

I would have to call myself a niche thinker, as my ideas seem to fall between those of an inventor (you know the kind from the commercials: a new kind of clothespin or ice tray) and an engineer, who has the specialized knowledge of machinery. I do not possess the depth of technical knowledge, but like to think that just SOME of these ideas are commercially or at least mechanically viable.

Human-powered train

Probably the most efficient of the easily-built human-powered means of transportation. A linked train of individual pods that can be hooked together (similar to railroad cars) with "stokers" in each pod would maximize power and minimize wind resistance. The train would be covered with a spandex skin that would cover the individual pods and link to the back of the pod ahead. A rubberized surface on the metal wheels would give traction on the slippery rails (similar to the wheels the maintenance trucks that currently ply the rails use).  Conceivably, dozens of these could be linked together to provide high-speed human-powered transportation between cities. A cone for the front and an aerodynamically "slippery" tail would be the only additional pieces necessary; these might resemble umbrellas.

Hase Kett-Wiesel makes a trike that might be adapted for use: it is a delta trike that can be linked together to form a train. Modifications could be made to allow rail wheels for a crude version of what I have in mind.

The problem in making this idea feasible would be opening the existing rail lines to platoons of individuals pedaling these trains, and integrating these pedal-powered trains into the system given the limited rails available.

Backyard Stirling cycle engine

By mounting reflectors to a sun-facing wall of a house and focusing them on a thermally absorbant surface no larger than a backyard BBQ grill or 55 gallon drum, one could take advantage of the natural temperature difference between the heated surface and deep below the surface of the ground (a thermal reservoir of naturally cooled rainwater) and generate electricity. A large biomass gass production pond/tank could provide gas to run the unit at night. The electricity generated could be stored as hydrogen. A mass storage of electricity as nominally-pressurized hydrogen could also be accomplished in a vented underground vault with a large bladder. 15slpm=1000W

Avalence technologies has patented a high-pressure electrolysis system that produces hydrogen gas at 10,000 psi. Honda makes a fuel-cell powered car. Now if banks will just loan one enough to get the Hydrofiller and the car; the savings in gasoline over a year might just be enough to finance the difference. One would still have to buy/generate the power to run the electrolyzer, however.

Human-powered helicopter

Anaerobic power would assist the initial ascent, and this should involve the arms, chest and shoulder muscles. A rig that incorporates the upper and lower body power and an adjustable attack of the rotor blades could allow such a helicopter to get off the ground.

Pulse Jets

There are some interesting pulse-jet sites on the internet. Perhaps using two of these jets at the end of rotor blades one could make a helicopter with little torque reaction and therefore little need for a "tail rotor" of any sort for anything but maneuvering. The pulse jets seem to run on natural gas or propane, so perhaps gas could be fed up the rotor axle (assuming a bearing able to hold compression on the rotor head) and out through passages in the blades themselves to power the jets.

SATS (Small Aircraft Transportation System)

NASA has funded research that could lead to a fleet of small, safe jet planes that could serve as a type of short- to medium-range "air taxis". The planes would use computers to show an illuminated "highway in the sky" and "synthetic vision" to aid navigation at night or in low-visibility conditions; have small, highly-efficient turbofan engines (much like those used on the cruise missile); and have a parachute in case of uncorrectable pilot error or pilot incapacitation. Eclipse aviation is just one group working on planes that could be useful in this market.

Gyrocopters

A balancing system not unlike those used on washing machines could be attached to the controls of a gyrocopter to prevent the "porpoising" that leads to the most dangerous condition for this inexpensive and otherwise very safe form of individual air transport. A small turbofan might also be used for the gyros, as well.

Improving the economics of solar cells

Focusing sunlight on solar cells could vastly improve the output per square inch of solar cells. New cells are becoming available that promise to make solar cell electricity more efficient. Perhaps a focusing mechanism could be built onto a sun-facing wall of a house. It remains to be calculated the amount of energy falling on any square foot of a south-facing wall during a day, however.

Rating Pistol and Rifle Kill Power

A few years back this idea hit me that kinetic energy and momentum alone were not sufficient indicators of the effectiveness of a round. It occurred to me that momentum AND velocity needed to be considered, and the idea in my mind was born. I was at the same time relieved (that I was not the only person crazy enough to think of the idea) and disappointed (I was not the FIRST) to find after a recent internet search to find that at about the same time I was doing my initial calculations, someone else was putting forward the same idea. I will not argue that the first the internet world heard of the idea was from a Mr. James Hall. His work can be found here.

http://www.xmission.com/~fractil/math/kp.html

James Hall introduces the idea of "kinetic pulse," or "kill power," and though I cannot lay claim to the original idea (and perhaps, he cannot either -- it is entirely possible that someone has put this forward before the internet and Google came along), I hope to add pieces Mr Hall did not include to the discussion.

But first, the obvious question the reader will ask is, "With momentum and kinetic energy already being calculated, is the calculation of kill power even necessary?"

The short answer is, of course, yes. It has long been hid in the discussion of "big, heavy bullets" for large game. Now, those big, heavy bullets show their superiority in some cases, when backed by the powder necessary to propel them at a velocity that maximizes their impact. One has the gut feeling that the 500 S&W is superior to many rifles in a close-in engagement with a grizzly because of that big, heavy bullet, but never before has that person had any numbers to back up the feeling AND for the unlucky person who runs into said bear, the experience. It should be noted that the kill power more accurately reflects what hunters have found in the field, under real conditions than looking either at kinetic energy or momentum alone. Experts may disagree here and there, but when the kill power is compared to what is found in the real world, one cannot help but wonder how it has gone unnoticed for so long. My strongest argument in favor of James Hall's kinetic pulse, or kill power, is the collective experience of modern shooters. This type of real-world analysis shows that Mr. Hall is on to something even if the physicists cannot explain it. It is to them we will leave it, but I hypothesize as a layman, especially looking at units that contain cubic feet per second squared, that it has something to do with a relationship between the rate of compression of tissue (variously described as hydrodynamic/hydrostatic shock) and the mass squared per second applied to it: the compression provides the backdrop for the knockdown power.

So let me add my contribution to Mr. Hall's seminal work.

First: shooters and gun nuts need a unit specifically for bullets and ballistics. I propose the AuE (pronounced "owie!"), which is one grain squared feet cubed per second cubed.  Simply put, this is the momentum of a bullet times the kinetic energy of a bullet. Using these units allows MUCH simpler calculation and comparison to existing bullets and load velocities from standard sources without conversion to slugs, kilograms, or other units outside the realm of experience of most shooters. The name AuE is a play on my own last name: Goldie, but the pronounciation of it declares its purpose. I am aware that using grains ignores the difference between the weight of a grain of material and the mass of that material, but when we start handloading bullets on the Moon or Mars, I'll revisit this subject. Since Mr. Hall has done all the work except to provide the name of the unit that we all can quickly calculate, I'll get on to my next contribution.

Second: I propose that there is a direct correlation between the killing power of a cartridge and the weight of the game (okay, let's just include humans as "game" for the sake of argument here). I will call it the Goldie Proportionality or Goldie Linearity. Multiples of ten increases in weight correspond to multiples of ten increases in killing power to effectively kill that game. I also postulate that multiple of ten increases in killing power result in a logarithmic increase in the probability of first shot incapacitation. I will provide an example below. Leaving aside questions of bullet design (obviously, hollowpoints will expand and expend more energy on targets a round-nosed bullet would be likely to pass through) and shot placement (a .22 between the eyes will be more effective than a .357 to the earlobe), it is nearly miraculous--or just a cosmic coincidence--that the calculated kill power is directly proportional to the weight of the game commonly taken with it. An example will illustrate my point:

Consider the .45 Auto, the venerable and proven man-stopper of WWII. Humans weigh in at an average of about 160~190 pounds. The .45 has a calculated kill power of  roughly 2 x 10^13 AuE. Working down the weight of "game", let us consider a large-sized, domesticated tomcat, at (conveniently chosen for our argument) 17-18 pounds--roughly one-tenth the weight of a human. One would hardly argue about the nearly perfect choice of a .22 rifle for dispatching the cat quickly. (As I type this I have a tomcat lying in my lap, so please take no offense, cat lovers!!) Coincidentally, a .22 LR has about one-tenth the kill power of the .45: 1.5 x 10^12 AuE. Going down to one-tenth the weight of a tomcat is the crow, weighing in at just over a pound--slightly less than one-tenth the weight of the cat. Again, the best weapon of choice for the crow--the .25 Beeman Silver Bear pellet fired from the Beeman Crow Magnum IV--has about one-tenth the kill power of the .22 LR, 1.9 x 10^11 AuE.

Still not convinced? For a nearly guaranteed one-shot stop on a good-sized human with a bad attitude, a .41 Magnum does very nicely, with a kill power of 6 x 10^13 AuE. For a proportionally big and bad Kodiak bear at 2000 pounds with ten times the heft, the 338 Winchester Magnum with a kill power with just over ten times times the kill power (6.5  x 10^14 AuE) would be a good choice.  Stepping up to hippos, rhinos and elephants that can range up to ten times the weight of a Kodiak bear, the rifles with ten times the kill power become the one-shot stoppers:  the King here is the 700 Nitro Express (7.3 x 10^15 AuE!! Geez, how do you even STAND the thought of firing that thing??). Coincidentally, the 700 NE has ten times the kill power, and and a little more kill power than the .50 BMG (6.4 x 10^15 AuE) at the kind of ranges where you are close enough to get a clean shot, but not too close to get a second.

As far as the logarithmic increase in probablity of first shot incapacitation, I think one would do well to consider the probability of stopping

Third: I'm throwing in my own derived method of calculating velocity of a bullet downrange as a function of ballistic coefficient and distance. If nothing else, this simple calculation can be used by the layman to closely approximate a bullet's velocity at a specified distance without having to refer to ballistics tables. I have tried it on a variety of bullets and velocities, and the results have been pretty good. Your mileage may vary.

So let us have a look at the data.

So now that we have a unit and some figures to work with, let's add this: to have a 9 out of 10 chance of achieving first round incapacitation, one must apply approximately 1 x 10^11 AuE per pound of target. To achieve 99 out of 100 chance of achieving first round incapacitation, one must apply 1 x 10^12 AuE (or, one Tera AuE) per pound of target. I suggest this rule of thumb only by what we know about home defense pistols and military rifles: a lot of home defense pistols lie in the 1-3 x 10^13 AuE range, and we presume they are intended for approximately 200 pound targets. Military rifles are MUCH more effective against human targets, and are the next order of magnitude above them, with a majority in the 1-3 x 10^14 AuE range. Again, this does not take into account shot placement or bullet design, but it gives one an idea about where to start theoretically when matching a weapon to the intended target.

Lastly, if you have read this far, you might want to jot down this handy little formula. One might find it elsewhere on the internet, but a cursory search did not turn it up. It is the formula to approximate the velocity of a bullet at any distance from the muzzle as a function of muzzle velocity, distance downrange, and ballistic coefficient. It seemed to agree well with the tables in the back of the Speer Reloading Manual credited below.

Vdownrange=Vmuzzle x e^-(.00034*d/b) ; where V is velocity, d=distance in yards and b=ballistic coefficient

NOTE: Most of the above data was taken from the Speer Reloading Manual for Rifle and Pistol, Vol. 13. Where data was not in the manual it was gathered from different sites on the internet: Hodgdon's site provided a fair amount, and the sites of individual makers where their products are explicitly listed.

NOTE: For all these rounds I have considered MUZZLE VELOCITY only. By applying the above formula and entering the calculated velocity into the formula for kill power, one can see that not all rounds are created equal when it comes to reaching out and touching the target. Take, for example the 50 AE (Action Express) 325 grain hollowpoint pistol bullet with a ballistic coefficient of .149 and the 30-40 Krag with a 165 gr. Speer boat-tail, spire-point bullet, ballistic coefficient of .477. They have nearly identical kill power at the muzzle, 1.69 x 10^14 AuE and 1.68 AuE, respectively. At 100 yards, the velocity of the 50 AE is down to 1174 fps, whereas the velocity of the 30-40 Krag is down to 2150 fps.  The kill power of the 50 AE is down to 8.55 x 10^13 AuE (about the kill power of the 22-250 at the muzzle), while the kill power of the 30-40 Krag is 1.35 x 10^14 (about the kill power of the 30-30 Winchester). At 300 yards, the difference is even greater: the 50 AE is down to about 743 fps, while the 30-40 Krag sails along at 1864 fps. Now, the 50 AE hits like a 40 S&W (2.17 x 10^14 AuE -- still no slouch, but definitely down from its former majesty!), while the highly-esteemed deer-hunter hits like a 22-250 (close to a 357 Magnum from an 18" barrel -- or your standard lever-action rifle in .357 Magnum). This illustrates that the big pistols have rifle-like power at short range for self-defense against the great bears, but should not be considered the primary weapon for your Alaskan hunting trip. Oddly enough, long, large-bore, aerodynamic bullets like that from the .50 BMG have VERY high ballistic coefficients, and do well on long shots: the .50 BMG from 3520 yards--TWO MILES--has the kill power of a 454 Casull fired point blank.