Not that I'm expecting any replies given the thread's age, but for future reference of any interested party... > At sea level it has vurtually no advantage, it

Not that I'm expecting any replies given the thread's age, but for future reference of any interested party... > At sea level it has vurtually no advantage, it’s not until Tye rocket ge s to thin air that the Aerospike efficiency is higher. There's more to it than this. Almost all practical rocket engines will have nozzle area ratios sized for altitude rather than sea level. That is to say, actual design nozzle area ratios will be significantly higher than the optimal ratio for ground level. This implies overexpansion losses at low altitude. The higher the area ratio, the worse this effect is. Rockets are designed this way because when you consider the mission-average Isp, it's better to reduce the underexpansion losses at altitude through higher area ratio and eat the overexpansion losses at low altitude than to optimize for liftoff conditions. An ideal aerospike lets you run a very high geometric area ratio with reduced overexpansion penalties. So it's conditional as to whether the aerospike "has an advantage" at sea level. If you are running a large enough area ratio, then compared to an equivalent area ratio bell, the aerospike will minimize the overexpansion losses at lower altitude, and additionally it will have reduced unsteady pressure loads due to avoidance of internal shock-induced separation, the way you would with a bell. The limiting area ratio for a bell nozzle is usually this internal shock separation criterion, whereas that constraint is removed for the aerospike. So at high enough area ratio, the aerospike could indeed have a low altitude benefit over an equivalent area ratio bell. As you point out, in practice, this effect doesn't tend to buy you a large net difference in mission-averaged Isp, particularly with staged rockets. Also as you correctly indicate, the largest mission-average Isp benefit for an aerospike is when the engine fires over a large enough range of altitude (e.g., SSTO) and when you can maximize the geometric area ratio. Such a case would also include the Shuttle, where an aerospike could have made a meaningful mission-average Isp difference, though for the same cycle parameters as the RS-25/SSME it likely would have increased engine weight. Also note that assuming you truncate the spike (as all practical aerospike engines would be designed), a high area ratio aerospike configuration would be shorter than the equivalent area ratio bell.