Wednesday, October 17, 2018

Travel theory

It is somewhat surprising, but to a certain extent we can calculate just how much it would be worth to have flying cars of various types. There is a research literature in travel theory, which is the study of how much people travel in various environments in different modes. It is mostly used in road and transit planning, but it gives us data and a point of departure. Here is the kind of thing you will find: this graph shows that as long-distance travel becomes more convenient, people do more of it:

Andreas Schäfer, Regularities in Travel Demand: An International Perspective, J. Transportation and Statistics, Dec. 2000

One would expect that if flying cars were available, people would make even more, even longer trips. But the surprising, unexpected empirical finding from travel studies is that people in all these societies spend about an hour a day travelling, whether they are in Zambia walking barefoot or in the US riding in an air-conditioned car. Some people travel a lot more than others within a given society, of course, but the average across a given a society is just over an hour—apparently a human universal.

To get a handle on how much people might travel under situations more advanced than ours, we can fit a curve to the data and extrapolate to longer trips and use it in calculations for faster transport modes:

For Americans, this is almost entirely by car. It turns out that there is another more-or-less surprising universal: your car does 40 MPH. For virtually any trip, of any length, the effective speed of a car as measured by the time taken to go the point-to-point distance as the crow flies is 40. You might think that you could do better for a long trip where you can get on the highway and go a long way fast; but again, the road system is essentially fractal. The big highways, on the average, take you out of your way by an amount that is proportional to the distance you are trying to go:

 Now the really interesting thing is that we can combine these two functions and derive the value to the average American, as measured in the amount of time they are willing to spend, of getting to whatever destinations there may be at a given distance from where they live:

There are two features of this graph that have at least intuitive explanations. The first is the peak in trips under ten miles. This is due to a combination of the low (time) cost of such trips, and a shadowing effect. If there is a McDonalds 5 miles from your house, you aren't going to go to one 10 miles away. To the extent that many destinations are alike, the near ones “shadow” the value of the far ones. The other interesting feature is the sort of hump going out to 50 miles. This is probably a daytrip phenomenon, together with the kinds of destinations for which people will make a trip of that length: a ballpark, a hospital, a restaurant fancy enough for an anniversary, etc. But in any case this is the empirically determined value to people, as revealed by their willingness to make the trip, of destinations at various distances.

Now we can design some flying cars—at least specify how close to home they can take off and how fast they can go. Let's take three designs to cover the spectrum: a helicopter-like one that lands in the driveway but can only do 100 knots; a convertible airplane that can do 200 and land on a short private strip or straight stretch of road; and a jetcar that can do 400 but has to be flown out of a full-fledged airport. Here's how they compare with a car, noticing that for many short trips with the latter two you never take off at all but just use them in car mode:

The next step is to substitute these travel times back into the value equations and find out how people would travel differently with flying cars of these types, and how much it would be worth to them. At short distances, the helicopter (or pure VTOL) dominates:

(Note that for these distances, you never actually fly the jetcar!)

This is the obvious advantage to a flying car, and the one most people are thinking of when they imagine a VTOL type: the ability to make the kinds of trips you normally do make, faster. But perhaps surprisingly, the numbers show that that's not where the major value would actually be:

When you look at longer distances, the jetcar dominates. The difference is that you would make a lot more long trips than you do now. Jevons rules. These are higher value trips but are too expensive in time to make very often with a ground car. Note that the value of having the given vehicle, as compared with a car, can be determined by taking the total area under the curves. The reason that the curves for the flying cars appear to represent less value for trips less than 20 miles or so is that you'd be taking fewer trips under 20 miles if you had a flying car—you'd be taking longer ones that were of more value to you instead.

We are now in a position to evaluate the value of any flying car, at least as specified by a latency number (the number of minutes added to a trip by having to go to an airport, convert car to plane, etc.) and a speed. The result is expressed as a multiple of the value of having a ground car:

Value of a flying car represented as a multiple of the value of a ground car, as a function of speed and latency (overhead time per trip).

The same chart, in a more easily read-out-able form.

A jetcar that was a VTOL you could fly from your driveway and make long trips at 400 MPH would be worth 7 times as much as an ordinary groundcar. The jetcar in the previous graphs, the convertible that did 400 but had an overhead of an hour per trip, has about half that value, 3.5 times that of a car. A fast prop-driven convertible (250 mph) would be about 2.5 times as valuable as a car, and a slow one (100 mph) only about 1.4, if they had to be flown from airports. That's roughly the same increment to the value of a car that you get from being able to drive to an airport and fly commercially at 400 knots, but incur a three-hour overhead in addition to actual flying time.

In theory if you would pay today's average of $35,000 for a groundcar, a fast VTOL jet car you could fly from your driveway would be worth $245,000, as far as pure travel time value is concerned.

Its value as a status symbol remains to be seen.

Tuesday, October 16, 2018

Crystallized space-time

There's an interesting article over at Nautilus about a new theory of black holes, or rather a theory in which there aren't black holes at all, but a phenomenon based on a bunch of quantum effects instead of relativistic ones.
...George Chapline, a physicist at the Lawrence Berkeley National Laboratory, doesn’t expect to see a black hole. He doesn’t believe they’re real. In 2005, he told Nature that “it’s a near certainty that black holes don’t exist” and—building on previous work he’d done with physics Nobel laureate Robert Laughlin—introduced an alternative model that he dubbed “dark energy stars.” Dark energy is a term physicists use to describe a peculiar kind of energy that appears to permeate the entire universe. It expands the fabric of spacetime itself, even as gravity attempts to bring objects closer together. Chapline believes that the immense energies in a collapsing star cause its protons and neutrons to decay into a gas of photons and other elementary particles, along with what he refers to as “droplets of vacuum energy.” These form a “condensed” phase of spacetime—much like a gas under enough pressure transitions to liquid—that has a much higher density of dark energy than the spacetime surrounding the star. This provides the pressure necessary to hold gravity at bay and prevent a singularity from forming. Without a singularity in spacetime, there is no black hole.
The theory is far from mainstream, but if supported by actual data, has the potential to upend a whole lot of astrophysics. But what caught my eye, or rather mind, when I read it was its similarity to a passage in a science fiction story from 1930:
"It is not matter at all, in the ordinary sense of the word. It is almost pure crystallized energy. You have, of course, noticed that it looks transparent, but that it is not. You cannot see into its substance a millionth of a micron—the illusion of transparency being purely a surface phenomenon, and peculiar to this one form of substance. I have told you that the ether is a fourth-order substance—this also is a fourth-order substance, but it is crystalline, whereas the ether is probably fluid and amorphous. You might call this faidon crystallized ether without being far wrong."
"But it should weigh tons, and it is hardly heavier than air—or no, wait a minute. Gravitation is also a fourth-order phenomenon, so it might not weigh anything at all—but it would have terrific mass—or would it, not having protons? Crystallized ether would displace fluid ether, so it might—I'll give up! It's too deep for me!" said Seaton.
"Its theory is abstruse, and I cannot explain it to you any more fully than I have, until after we have given you a knowledge of the fourth and fifth orders. Pure fourth-order material would be without weight and without mass; but these crystals as they are found are not absolutely pure. In crystallizing from the magma, they entrapped sufficient numbers of particles of the higher orders to give them the characteristics which you have observed. The impurities, however, are not sufficient in quantity to offer a point of attack to any ordinary reagent."
"But how could such material possibly be formed?"
"It could be formed only in some such gigantic cosmic body as this, our green system, formed incalculable ages ago, when all the mass comprising it existed as one colossal sun. Picture for yourself the condition in the center of that sun. It has attained the theoretical maximum of temperature—some seventy million of your centigrade degrees—the electrons have been stripped from the protons until the entire central core is one solid ball of neutronium and can be compressed no more without destruction of the protons themselves. Still the pressure increases. ..."
That's from Skylark Three, by E. E. "Doc" Smith. All the details are different, of course, and people still referred to the stuff of empty space as the luminiferous ether instead of "space-time," but you get the idea.

Thursday, October 11, 2018

Ammonia, the fuel of the future

(You may, if you wish, sing that to the tune of Columbia, the Gem of the Ocean.)

Back in 2009, at Foresight, I wrote a post on the prospect of ammonia as a fuel, basically as a hydrogen carrier:
What will your car run on in 2020 or 2030? What form of energy storage and transmission will allow intermittent energy sources, such as wind and solar, to be a viable input to the economy?
There’s a good chance, of course, that cars will still run on gasoline — its demise has been predicted early and often — but there are also lots of reasons that petroleum will not be a sound basis for a rapidly-expanding economy. We’ll want to save the hydrocarbons as a feedstock to our nanofactories…
Why not batteries? For cars, in particular, batteries are heavy but they are also inefficient. You lose a lot of energy by storing it in a battery and taking it out again. Almost certainly, nanotech will allow us to build lighter, more efficient batteries, or their equivalent, such as ultracapacitors. But that comes with a major drawback: the higher the energy density of a closed-cycle battery, and the more quickly you can charge it, the more quickly it can release its energy. In simple terms, a really good battery would be a bomb.
The answer to both weight and safety concerns is an air-breathing battery. Only storing one of the two reagents saves weight, and means that the potential energy isn’t in the battery, but in the battery and a large volume of air.
The answer has always been hydrogen. (I assume hydrogen in Nanofuture, for example.) Hydrogen is very light. It’s fairly safe — since it’s lighter than air, a leak dissipates rather than forming an explosive mixture. It can be generated from water by electrolysis and used in fuel cells with decent efficiency (about twice that of internal combustion engines). It seems likely that nanotech will give us ways to separate and recombine hydrogen that produce a very high-efficiency energy-storage cycle.
But there are some drawbacks: hydrogen is bulky, though light, and it needs to be stored at very low temperatures. It’s a real pain to deal with, and that means it’s expensive to deal with. Storage and transportation quadruple the cost of hydrogen as a fuel (see the bottom of the last page here).
Turns out the best way to deal with hydrogen is to use some highly hydrogen-bearing compound, such as methane. This is in wide use as a fuel, in the form of natural gas. (Alternative forms are the alcohols, such as methanol and ethanol). But we are still stuck with that carbon, and not only does it produce CO2 emissions but intermediate products such as CO tend to poison present-day fuel cells.
 An often-overlooked alternative is (anhydrous) ammonia, NH3. Because it’s a polar molecule, it’s easier to liquefy than methane (-33C as opposed to -162C). A liter of ammonia contains more hydrogen than a liter of hydrogen. It’s easy to crack into hydrogen and nitrogen — nitrogen can be emitted without worry since it is already 78% of the atmosphere. You could burn ammonia in a big, powerful, fuel cell, or even a big, powerful internal combustion engine, indoors without the kind of problems you’d get with carbon-bearing fuels. There’s a fairly easy path to using ammonia as a fuel. It’s already produced in major industrial quantity and there are thousands of miles of ammonia pipelines. It’s a good fuel for current-day fuel cells, and near-term nanotech is likely to improve the catalysts for all parts of the cycle.
 Looks like I may have gotten one right, especially that last sentence. We note the following from Rice:
HOUSTON — (Oct. 4, 2018) — Rice University nanoscientists have demonstrated a new catalyst that can convert ammonia into hydrogen fuel at ambient pressure using only light energy, mainly due to a plasmonic effect that makes the catalyst more efficient.
A study from Rice’s Laboratory for Nanophotonics (LANP) in this week’s issue of Science describes the new catalytic nanoparticles, which are made mostly of copper with trace amounts of ruthenium metal. Tests showed the catalyst benefited from a light-induced electronic process that significantly lowered the “activation barrier,” or minimum energy needed, for the ruthenium to break apart ammonia molecules.
The research comes as governments and industry are investing billions of dollars to develop infrastructure and markets for carbon-free liquid ammonia fuel that will not contribute to greenhouse warming. But the researchers say the plasmonic effect could have implications beyond the “ammonia economy.”
The other development in the interim is that the technology for hydrogen fuel cells is getting within hailing distance of piston internal combustion engine power/weights. (But they ain't cheap!) So come 2030, who knows, you might not need that turbine after all.

Wednesday, October 10, 2018


Chapter 13 of WIMFlyC begins thusly:

Travel theory tells us that if we can make a flying car that only has five minutes of overhead and can do 250 knots once in the air, it would be worth about 5 times as much as a ground car. (250 knots is a speed limit in US airspace below 10,000 feet, so we will use it as a point of departure for speculation. You can't fly much over 10,000 feet without needing oxygen or pressurization.) What are the chances of building such a thing? How much power do we need, for example, to get 250 knots out of our flying car? Here's a graph of a wide range of 20th-century propeller aircraft, showing power vs speed. There's a huge variation in speed at any given power (and vice versa), but it seems possible to design one that gets 250 kts if you have more than 500 HP available:
This graph has an odd structure, apparently; there are two separate bands for single-engine planes, which are interleaved with two bands of twins. What's happening is that the high-power, fast singles are WWII fighters and the like, built with very different design goals from the small light private planes which make up most of the low end. The variation in power has a lot to do with aircraft weight, of course. Using the same engine, you would get much more speed in a single-seater with barely room for your flight bag than you would in a car-like plane that carries a family of four and their luggage. We can finesse the issue by dividing by the weight of the loaded aircraft. Here are power-to-weight ratios by airspeed:

You can see that the designs are much better mixed, all falling along the same “main sequence”.

A speed of 250 kts means that we need a horsepower number somewhere between 0.15 and 0.25 times the weight in pounds. You can see that the graph curves toward higher speeds at the same power loading over about 150 knots. This is due to the fact you use less and less power to produce a pound of lift the faster you go, so faster airplanes tend to be bigger and heavier. Let's estimate that with high-tech materials we can make the vehicle 2000 pounds and have it carry 1000 pounds of payload. That means we need somewhere on the order of 600 horsepower. And that's a problem: a piston engine producing 600 horsepower weighs on the order of 900 pounds. Airplanes with those statistics were produced, in the Thirties and Forties, but they were fighters and racers, more than half engine. We would be much better off with a turbine. The Lycoming/Honeywell LTS101-650C, for example, packs 675 HP in only 241 pounds.

I then proceed to argue that the flying car you would like to have, one that would get up into the range of airliner speeds while being able to land on your driveway, would have to have a turbine in it.

However, for the cheapo build-it-today autogyro version, we can probably get away with something different. One of the reasons that piston engines are so heavy in airplanes (my 0-360 gets 180 HP out of 250 lbs) is that they are directly coupled to the prop, and the cubic inches are to provide torque at a relatively low speed. The way to get high power at low weight is to have lower torque at high speed, and then gear it down. The Rotax engines used in most current gyros works that way, for example.

You could also get better power-to-weight by using a 2-cycle engine; Rotax makes a snowmobile engine that gets 150 HP out of 100 lbs. The major problem with 2-cyclers for aviation is that they do have a tendency to announce their end-of-useful-life by suddenly seizing up.

So what we would do in the gyro is to have two such engines, and no gearboxes. Instead couple the engines directly to generators, which feed electric propulsion and the rotor motors. (Today's electrics have a remarkable power to weight, getting up to several HP/lb.) You have some batteries, which provide you with a hole card; but you have an even bigger one: you're an autogyro. Just run your rotor motors in regenerative braking mode on the way down, and you can regain quite a bit of the energy of your altitude. That and your second engine give you a decent margin of comfort.

So, yes, the flying car of the future will feature a turbine, or maybe something like a fuel cell, after a bit more technological progress. But we can still build a usable one today with what we have.

Tuesday, October 9, 2018

The autogyro as flying car (part IV)

In Where is My Flying Car (Ch. 11), I examine the question of whether you'd want a plane that could fold up into a car and be driven on the streets, or a VTOL type (e.g. a helicopter) that could take off from your driveway and land anywhere. Of course, what you really want is both, but you can't have everything and you have to make some compromises.

Both kinds date from the 30s. The first fully functional fixed-wing flying car was Waldo Waterman's 1937 Aerobile. Waterman in 1932 had built and flown the world's first tailless (“flying wing”) airplane. This was incidentally also the first plane with modern-arrangement tricycle landing gear, with two wheels in the back and a steerable nose wheel. This is considerably more stable and resistant to ground-looping in a crosswind than the old “tail-dragger” configuration. The Arrowbile was by all accounts relatively easy to fly. The wings could be removed, and the fuselage part driven around as a car. Five were built; unfortunately, on top of the difficulty of trying to sell them into the Great Depression, Waterman's financial supporter and promoter died unexpectedly, Waterman himself had a serious illness for a year, and then like almost every other major aviation figure was swept up in the WWII military aviation surge.
Similarly, in the same era Pitcairn had gyros that could land anywhere (most notably the White House lawn). Then of course ten years later there were actual helicopters.

In Chapter 17 I work out what you would like your future flying car to be like, but that is set against some projections of future technology. The autogyro seen in the previous post was carefully designed to be within the constraints of current-day technology at a level affordable to a car owner. In particular, it was designed to use a piston engine instead of a turbine (@ $500,000). The devil is in the details, of course, but it seems like if it were mass-produced, you could get the cost of such a gyro down below $100,000.

That's about three times the price of the average new car. Our chart tells us that if you can push the cruising speed up to the 125-150 kts range, it will be worth about three times as much as a ground car. That's the same, in terms of travel time, as a private jet which could do 350 en route but required a trip to the airport and a total overhead of an hour per trip.

Going by current prices, the jet (or a turboprop with comparable speed) would cost a couple of million, so in current tech the latency seems easier to finesse than the speed.

There remains the issue of the infrastructure necessary. The automobile did not get to its current useful state without an enormous societal investment in roads, up to and including the interstates. Considerably less would be necessary for gyros, and there is a good deal less of a public goods problem involved. Put a small pad at your house, and you have zero-latency access to the air; put one at your business, and you have made yourself available to a class of well-to-do customers. 

The only really tricky thing about the whole business is regulation and air traffic control. There are about 20,000 airports in the US, of which roughly 5000 are open to the general public. Only 500 or so offer commercial flights. In fact there are only about 6000 commercial airplanes. For comparison, there are about 3000 counties in the US, so there are on average between one and two public airports per county, and six or seven including private airstrips.

There are on the order of four million miles of roadway in the US, of which about 2.6 million are paved. The Interstate system comprises about 50,000 miles of this, and that and 100,000 miles of major state highways carries about half the traffic (vehicle-miles).

The contiguous 48 states have an area of about 3 million square miles. There are about ten miles of altitude accessible to aircraft (two to non-pressurized ones with normally aspirated engines—you and your engine get breathless at about the same point). Under current regulations airplanes need 1000 feet of vertical separation and 5 miles of horizontal (back of the envelope rule of thumb—actually the regulations are quite complex). These regulations are based on a technology where the pilot is looking at an altimeter and controlling his altitude manually (indeed flight levels are defined by barometric pressure, not actual height), and maintaining horizontal separation by verbal interaction with air traffic controllers. Physically, planes can safely fly much closer together if they are going the same speed and direction; think of geese flying in a V-formation. But let's take the current regs as a point of departure.

If you merely parceled out the airspace in lanes at these separations you would have on the order of 30 million miles of high-speed highway—200 times what we have on the ground.

That would mean there is room for six million aircraft in the air at one time (one million non-pressurized). If you cut the separations to a mile, which wouldn't be hard for good electronic controls, you'd have 150 million miles of lanes and the same number of aircraft in the air at once. That's more than there are cars on the roads.

Moulton “Aerocar” Taylor was of course right; the existing air traffic control system would completely break down long, long before that many private planes got into the air. It is surprisingly antediluvian for the twenty-first century. In an era when the distributed control of the internet routes and switches literally trillions of packets of information per second all over the planet, each interaction with ATC is done by voice in English with a live human being. This makes for a system that is often running at the outer edge of its capabilities. Recently (Sept. 26, 2014) a disgruntled employee cut some cables in the Chicago Center and set fire to the building. This created a 91,000 square mile hole in the ATC system. More than 1000 flights were grounded while controllers scrambled to reach alternate facilities as far away as Kansas City. Besides being somewhat fragile and running near capacity, our current ATC system is not easy to expand. It would be simply incapable of handling the orders of magnitude more traffic that generally owned flying cars would involve.

Watch a flock of birds land on and take off from a field, or a seagull tornado doing a continuous rolling dive on a patch of delicious flotsam. It is clear that no possible human ATC could handle such collective flight patterns, but also clear that they are possible with purely local distributed control, using senses and reflexes not impossibly more capable than our own.

When you fly on a clear night you see quite a few more other airplanes than you do in the daytime. That's because they have big bright anti-collision strobes which are visible 25 miles away. With car-density traffic, such strobes would make the sky a confusing Las Vegas-like lightstorm, but they could be replaced with radar-frequency beacons that encoded your car's position, altitude, and course. Your autopilot could read these all in real time and know its situation vis-à-vis every other aircraft nearby at least as well as the seagull does, but on a scale 1000 times as large. We need, roughly, a factor of 20 for our car's speed (500 as opposed to 25 mph), leaving us with a factor of 50 to account for being slower to turn than the seagull. Since we are not intending to be dogfighting, but just merging into and out of traffic flows, this should be plenty.

There are roughly 3 million square miles in the contiguous USA, and 200,000 cellphone towers. That makes one per 15 square miles, for an average distance apart of 4 miles. At cruising altitude you are in view of ten to a hundred of them most of the time. Put a box on each one that looks for and talks to all the aircraft in its area, very similarly as the cell tower already does for pocket phones. Add that to GPS and your flying car can always know exactly where it is, and where every other aircraft in the same state is, to within a foot. Add that to inter-car communication and all that remains is to work out the rules of the road.

It turns out that something like this scheme has been implemented for the North American airspace under the somewhat opaque acronym of ADS-B, for Automatic Dependent Surveillance — Broadcast. Instead of using the 200,000 cellphone towers, it uses 634 custom government-run ground stations. These provide coverage over much, but not all, of the continental US. By 2020, all aircraft operating in certain high-traffic areas (essentially the same ones that require a radar transponder today) will be required to be equipped with ADS-B-Out, consisting of a GPS reciever and a transmitter that broadcasts the plane's position and altitude into the system. Whenever that is done, about once a second, the system transmits position information about traffic in a “hockey puck” 15 miles wide and 3500 feet thick around the airplane back to it. Separate equipment to receive and display this information in your cockpit, ADS-B-In, is available but not required.

As it stands today, the ADS-B system provides air traffic controllers with more complete and accurate information about aircraft, and provides pilots with information they would not have had at all. To some extent, it is an existence proof that a decentralized system is possible, and is a step in the right direction. However, it basically replaces the existing radar network and feeds into the existing centralized air traffic control system. It would still require a major revolution at the ATC level to accomodate generally-used flying cars.

The best chance that has of happening today is by growing out of a decentralized system for drones. There are now ten times as many drones as manned aircraft. The FAA tells us about it:

How will a UAS traffic management system (UTM) work? UTM is how airspace will be managed to enable multiple UAS operations conducted beyond visual line-of-sight (BVLOS), where air traffic services are not provided. The FAA, NASA and industry are partnering to develop UTM to support the real-time or near-real-time organization, coordination, and management of primarily low altitude (< 400 ft AGL) UAS operations.

At the moment all it supports is automatic notification of airports of drone activities in the area, but given the pressure (and an increased willingness to experiment with drones), we may see some real advances.

On the other hand, I have no idea at all how to fix the regulatory logjam.  Sorry!

Monday, October 8, 2018

The autogyro as flying car (part III)

The first time I took a flying lesson in a regular fixed-wing airplane, my flight instructor had me taxi across the airport to be sure I could use the pedals to steer the plane. Then we lined up on the runway and he said, "Ok, now take off."
Taking off in a fixed-wing airplane is fairly easy; you shove the throttle to full power and steer in a straight line, and when the airspeed indicator says you're going fast enough, pull gently back on the yoke and away you go.

In a gyro, not so much. First, line up on the runway and push the stick full forward. Then, holding the brakes, move the throttle up to about 2000 RPM, or the engine will stall when you do the next part. Release the rotor brake (wheel brakes still on) and engage the pre-rotator. You have to slowly edge the throttle up as the rotor accelerates, until it reaches 200 RPM. Now, in quick succession, release the wheel brakes, pull the stick full back, advance the throttle up to about 4000, and steer straight down the runway. As you accelerate, the relative wind will bring the rotor up to about 400 RPM. This enough to begin generating lift, which pulls you up onto your back wheels, doing a wheelie down the runway. You must accommodate this instantly with the stick; otherwise the angle change of the rotor shaft with the wheelie will tilt the rotor too far back and pull you over backwards.
Congratulations! you have now formed a wing. Still balancing on your back wheels, use it to take off. Continue accelerating down the runway, noting that the torque from the propeller will be trying hard to make you turn left; counteract this with pressure on the right rudder pedal.

The best way to visualize the rotor disc as a wing is to see that it induces the same lift-producing circulation patterns as a solid wing, but notice that the airflow can go through the disc. As you see, the flow is coming up through the front and going down through the back part of the disc. This pushes up in front and down in back; but by the magic of gyroscopic precession, it tries to tilt to the right, so push the stick to the left to counteract it.

Back in the 30s, barnstormers in Pitcairn gyros used to take off from football fields, off the ground in 50 yards with plenty of room to climb out over the stands. For a flying car, you could easily regain the advantages they had -- a more powerful motor and a pre-rotator capable of running the rotor all the way up to flight speed.

But for a flying car to be used by the multitudes, you also want a somewhat more intuitively controllable vehicle. The problem with the gyro is that it is a pendulum hanging from the rotor, and any control input has a tendency to set it swinging, and swinging acts as an oscillatory control input to the rotor. This not only makes control more difficult, but can result in a queasy ride.

By far the major innovation in aviation in the past few years is the quadcopter drone, along with its variants. It sits in a very nice local optimum in flying machine design space; it only has 4 moving parts! The electric motors have a quick enough response time that you can control roll, pitch, yaw, and lift purely with differential power.

The major problem with the quadcopter as a flying car is that if you scaled it up to car size, it would need 1000 horsepower to do the kind of things that the toys do, and even so it would be extremely inefficient as a flying machine. But it seems possible to do yet another compromise and get some of the advantages of the quadcopter along with those of a gyro.

The basic ideas are
  • Make the rotors very light and stiff (but still Bensen-style teeter hubs). The rotors on helicopters and classic gyros are heavy, as they are used to store energy. Store it in a battery instead.
  • Put small (e.g. 10 kW) motors on the hubs. This would be nowhere enough power to take off vertically, but could prerotate and provide enough differential power for attitude control.
  • You'll need at least a forward-back control stick input on the rotor masts for different flying modes; if you add side-to-side you can use it to counter gusty side-winds without tilting the whole vehicle. With small light fast rotors, control response will be extremely faster than with one big heavy one.
  • There are of course separate propeller(s) for thrust (not shown). The struts act as wings to unload the rotors at higher speeds. Rotor drag goes way down edge on into the wind, but you lose lift and autorotation. Not a problem with the motors.
Now takeoff is a much more civilized proposition. Start the rotors up, accelerate down the runway, lift off. None of this pendulum stuff. Some back-of-the-envelope calculations indicate you should be able to get off the ground inside 70 feet, which is a short driveway or the diameter of a circular roof pad on a 50x50 foot house. (Just bury those damned electric wires!)
In cruise, you can afford to slow the rotors down and very likely do better than a helicopter, say somewhere between 125 and 150 knots. That will depend on how much engine you put in, of course.
And landing is as easy as falling off a log. The one thing a gyro does better than any other aircraft is stop. Just tilt the rotors back and the autorotation power goes way up because they are seeing more air. At the same time the force vectors give you a lot of that lift as drag. You pretty much stop dead in the air. All you have to do is arrange for that to happen just as you touch your driveway or rooftop pad.

In the next post, I will speculate on how and whether flying cars of this or similar design would make a big difference in the way people live, the way the private automobile did in the 20th century.

The autogyro as flying car (part II)

So to recap, by the 50s the autogyro had basically been forgotten, and it was the helicopter on your rooftop landing pad that was going to be your flying car of the future. The reason it didn't is that helicopters are expensive, and require a lot of training, and since you have to train in a helicopter, the training is expensive too. Your rental of an airplane as part of your flight lessons is on the order of $100 per hour; for a small helicopter, $500.

The reason that Pitcairn stayed so stubbornly attached to the idea of an autogyro is that the gyro is a compromise between an airplane and a helicopter, not only in capability but also in price. Let's look at the reasons why.

Gyros and helis both have a motor, but in the gyro (in flight), the motor only turns a propeller. The motor in a helicopter turns both the main rotor and the anti-torque tail rotor. In a gyro, the relative wind comes up through the rotor disc, both producing the torque to keep the rotor turning and lift. Since you have to keep the rotor tilted back to get the autorotating wind, some of that lift force acts as drag, requiring the separate propeller. In the helicopter, the rotor is tilted forward, so the lift force produces thrust.

One of the main components of the cost of a helicopter is the rotor hub, which even now is out near the edges of the envelope of technical capability. The hub is extremely complex; it has to be extremely precise—tiny fractions of a degree or millimeters of position matter—and it is under tremendous stress: the blades pull outward with literally tens of tons of centrifugal force. Imagine trying to build a mechanical clock that had to be accurate to a second a day, small and light enough to carry in a suitcase, but which would have railroad cars attached as the hour and minute hands. So the rotor hub is not only expensive to manufacture, but for safety must have constant maintenance by well-trained, intelligent, and motivated—read expensive—technicians.

One of the things we noted about the gyros in the 30s is that they lost their wings. Cierva's "direct control" rotor hub allowed the pilot to shift the axis of the rotor without changing the attitude of the entire aircraft. 

At this point, the hub of a gyro was just about as complex as a helicopter. It had fully articulated blades, with back and forward as well as up and down hinges. The rotor hub was mounted on what was essentially a universal joint; this gave it full cyclic pitch control. You tilt the axis of the hub and the resulting changes in angle of attack of the blades made them fly into a plane orthogonal to the hub axis. This was Cierva's second big ingenious contribution to rotorcraft technology, after the flapping blades that made the gyro workable in the first place.
Even with this hub, the gyro is still simpler and less expensive than an equivalent helicopter. The gyro has a propeller mounted in its engine shaft, whereas the heli has a complex gearbox that turns both the main rotor and the tail rotor. But the real simplification (and cost reduction) in gyros had to wait for one final really ingenious insight.
This was the invention of the “teeter hub” one-piece rotor by Igor Bensen in the Fifties. A lot of the complexity, and thus expense, of the rotor hub on both helicopters and autogyros was the fact that each blade had to be individually hinged both up/down and forward/back, and that the hinge had to withstand the enormous centrifugal force while remaining extremely precise with no play or looseness. Bensen realized that if there were only two blades, the hinged excursions of one were just opposite those of the other one. This includes not only the up/down flapping, but the forward/back precession, and indeed the cyclic angle of attack variation. The way this works is ingenious but mechanically simple, so the rotor can be one solid piece without the centrifugal force going through linkages, hinges, and bearings. This substantially lowers the cost and raises the reliability of the gyro. Unfortunately, you can't use Benson's trick for a helicopter, because it doesn't allow for collective pitch control.

There has been something of a resurgence of gyros in recent years, particularly in Europe, using the Bensen-style teeter hub and with a small enough engine to fit in a light-sport category. This brings the price down to luxury-car levels instead of up in the stratosphere with helicopters. (In the US, regulatory headwinds have nevertheless made them few and far between.) They are fun machines to fly but don't have as short a takeoff roll as the Pitcairn gyros. The Pitcairns had three times as powerful an engine, and would pre-rotate the rotor up to full flying speed before moving. The modern light-sport types use a lighter mechanism to bring it up to half speed and use the takeoff roll to bring it up the rest of the way. But they can still land on a dime.

The German-make Calidus is the only autogyro currently being produced that has an FAA type certification. If you want any of the 10 or so other ones in the market, you have to get a parts kit and build it in your garage.

Takeoff in a gyro is more difficult than in a fixed-wing airplane, but landing is easier. The ratio of takeoff to landing gyro accidents in the 30s bears this out (as does your author's personal experience). The most common accident in a plane is slipping, stalling, and crashing on approach. In a gyro, it is tipping on takeoff with a rotor ground strike. You are much more likely to walk away from rotor strike than an approach crash. In 1932 Fortune magazine carried an article that listed the ten worst autogyro accidents to that time — none of them fatal.

Gyros didn't catch on as a segment of aviation for a number of reasons. The first and most obvious is that they were superceded by helicopters. A gyro is in practice a compromise between an airplane and a helicopter; one manufacturer advertises that it “does 90% of the mission at 10% of the cost.” It's probably fair to say two thirds of the mission at one third the cost. In today's specialized commercial market it loses to the extreme cases for particular applications: airplanes for speed and fuel efficiency; helicopters for hovering and vertical takeoff. The advantages of the compromise were, in Zimmerman's words, “an airplane suited to the needs of the private owner.” A private car is likewise a study in good-enough trade-offs. 

In the next post we will consider the question of whether a gyro could actually be a good-enough flying car.