Am I correct in saying that it would benefit economy to create a crank that would allow variable compression and variable time at TDC?
It depends on the situation and there are trade-offs involved.
Three situations need separate discussion - traditional spark ignition SI (detonation limited), traditional compression ignition CI (fuel/air mixing limited), proposed "premixed Homogeneous Charge Compression Ignition" HCCI (reliability of ignition limited). I'll use VCR as an abbreviation for Variable Compression Ratio to save a bunch of typing.
A situation common to both SI and CI is that the combustion process depends on turbulence. It's more critical with CI where turbulence also has to mix fuel and air. But even with a SI engine, "squish" turbulence near the end of compression speeds up combustion a fair bit. A fast-burn engine with decent squish-bands (but not too much) will usually be more efficient and run better than one with an open low-turbulence chamber. How do you get squish ... by having the piston closely approach the head. But with VCR you want high compression in the situations where detonation is least prominent (low load) and this is your limiting factor for how close the piston can get to the head. At high load where detonation is more likely, you have the piston stopping further down the cylinder - reducing squish turbulence at the time when you need it the most. Not favorable ...
With CI it's even more critical; look at the shape of a TDI piston and how closely the part outside the bowl comes to the head and valves. If you stop the piston further down the bore then it destroys fuel/air mixing. Definitely not favorable.
Maybe there is another way of doing VCR without having the piston-to-head geometry change but I don't know of a way to do it that doesn't have other, bad, horrible-combustion-chamber-shape implications.
HCCI is another matter because it's not relying as much on squish turbulence to speed combustion or mixing. It doesn't need a turbulent chamber late in the compression stroke (only during intake stroke and whatever turbulence remains afterward, to complete air/fuel mixing). In this case, VCR could very well be the key for getting HCCI to operate successfully over a wide-enough range of speed and load and temperature.
I have a feeling that soon-to-come variations on gasoline direct injection are likely to wipe out whatever hypothetical benefit remains of VCR on spark-ignition engines. Mazda Sky-G will have 14:1 compression ratio - and its combustion chamber shape is almost diesel-like and very reliant on the piston very closely approaching the head, just like with a diesel. Beyond that compression ratio, there are diminishing returns and you start losing more due to heat losses anyway. Don't need VCR if you can run the high (optimum) CR all the time, even at full load!
Now, as for the "time near TDC" ... this is a lot more murky. With a normal engine, it's affected by the rod-to-stroke ratio. The "time near TDC" is always shorter than the "time near BDC". Manolis8 has a nifty design with the con-rod reversed which reverses this. So the question is whether you want more time near TDC or not. From all I can gather, this is somewhere in between an "it depends" and an "it doesn't matter".
If you have a combustion process that is "slow" or "ignition lag limited" etc., then having more time near TDC will give more time to get it done at a phase in the cycle where more work can be extracted. This favors longer rods or Manolis' reversed-rod arrangement. Diesel and HCCI come to mind here. BUT.
- The longer the hot gases sit around near TDC, the more heat they lose to the piston, cylinder liner, etc. So from this point of view, you need to spend the time near TDC that you need to spend, but once the combustion gets well established, you need to get the gases expanded pronto before they lose too much heat!
- If it is a premixed detonation-limited situation (SI engine) you don't necessarily WANT the piston to hang around near TDC too long. You need to get the expansion going so that the end gas is less likely to detonate. Formula 1 car engines - which are gasoline fueled - use this approach. Compression ratio is high, but after ignition, the expansion occurs so quickly that the end gas doesn't detonate. Apparently, beyond 12,000 rpm, detonation is almost impossible to occur. Those engines are not designed to have high volumetric efficiency at low revs - probably intentionally; this acts like a lower compression ratio. Note how high the idle speed is on those ...
With a SI engine, a fast-burn chamber and NOT spending more time near TDC seems more like the way to go. Get the ignition going (multiple spark sources, if needed), get the mixture burned pronto before it has a chance to detonate, and get it expanded before it pumps too much heat into the pistons and valves (and loses some of its ability to do mechanical work). The Mazda Sky-G engine has a very compact, confined, almost diesel-like chamber in the piston and they're using direct injection, which is probably/hopefully putting the fuel in the center of the chamber and away from the end gas. If there's no fuel in the end gas, it can't detonate.
Other random effects
- If you are spending more time near TDC then you're spending less time near BDC, which means less time for cylinder filling at high revs.
- Short rods (the implication of which is more time near BDC and less near TDC) introduce more secondary imbalance into the engine. Depending on the layout and number of cylinders, this may or may not be an issue. 4-stroke even-firing inline-4 ... big issue.
- Long rods need to be thicker and heavier to resist failure in buckling. That adds weight. If you want to spin the engine fast, that extra weight is not good. If you want to run diesel-like compression ratios (and a fast-burn chamber that raises cylinder pressures), buckling is a consideration. (Manolis' reversed-rod engine has them in tension ...)
- Of course, the effect on the overall height of the engine has to be considered. Long rods means taller deck height.
Smokey Yunick was always a fan of long rods. Nowadays ... in the hot-rodding world, there's no clear pattern. In the high revving motorcycle engines and Formula 1 cars, the rod/stroke is usually in the 2:1 range give or take. VW engines have short rods, which helps with buckling stress in the diesels ... even if the real reason is that VW is saddled with their 88mm bore spacing and they are stuck with long-stroke designs as a result, but they still want to not make the engine too tall, so short rods it is, rightly or wrongly.