answer:Oh this is near and dear to my heart. I had the misfortune of actually doing this analysis for my employer about 10 years ago. Virtually every manufacturer has built and tested units like this. Also FEV, AVL and a host of others. The problem is that sticky issue of physics. Here are the assumptions and requirements. You’re smart so I’ll let you do the math. You want the valves to open and close fast enough to operate in an engine turning 6000 rpm minimum. The mass of the valve is given. Ignore the solenoid actuator as we will make the valve the only moving element. The valve must open 10mm minimum to get the proper swirl and tumble in the cyclinder. Now do the math and calculate the acceleration required to move 10 mm in less than a couple of milli seconds. Now figure the force. F=ma. Now calculate the energy FxD. Now calculate the power based on the number of cylinders per second. The answer is 2 kW. Now figure the wires required to deliver that power. P= VxI 12volts into 2 kW – ~200 Amps. Let me repeat, 200 Amps! That is a battery cable going to your soleniods . Now you need some way to switch that current on and off quickly with no delay.for 100,000 miles IGBT drivers might work. Experimentally, we can do anything. the problem is the physics. We need to get that 2 kW at the valves. Our alternator is 75% efficient. Our solenoids are 80% efficient, our drivers and wires are 90%. So that means we need 3700W of electrical power from somewhere and expect to lose 1700W to heat. Some manufacturers actually ran their testing with external power supplies. But that’s cheating. :-p You can fiddle a little with the valves make them lighter, reduce the lift reduce the rpm etc. But in the end electrical power and heat are the limiting factors. There are many alternate designs. Variable valve timing. variable valve lift. Cam phasing Delphi and BMW have clever designs that do both lift and timing.. But the high initial cost is too great for the modest fuel economy gain. Everyone has a trade off. Cost vs % fuel economy. When that gets above 70 it is hard for customers to justify the purchase. Believe me if they could sell it, they would.