I got out my pencil to see when it may or may not be practical to use a steerable drogue chute to get back to the launch position. I have come up with relationships for the forward drogue speed Vf and descent rate Vd as a function of rocket altitude, downwind distance, glide ratio, and wind speed. These are boxed in red. With the sign conventions, all variables should have a positive value.

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With the forward velocity relationship if we achieve equality, we can get back to the launch site. If the velocity exceeds equality, we can get upwind of our launch site. In this case, I would program the drogue to spin in a loop then go upwind again.

Lets start with the denominator of both velocity equations. This must be positive. The glide ratio must be larger than D/H, the rocket distance/altitude ratio. The forward to downward gliding progress must exceed the rocket downwind/altitude ratio. If we have a glide ratio that is much larger than D/H, then the forward and downward velocities can be reduced.

The forward drogue speed relationship, upper red box, tells us that when the glide ratio gets really big, then then necessary forward velocity can be lower. Forward velocity always is greater than wind speed, which also makes sense.

The descent rate relationship, lower box, indicates that we will typically have a descent rate lower than the wind speed. This assumes that g is at least twice D/H, which is reasonable.

So now for some real world numbers. I know a lot about kites, but not parachutes so I googled for some values.

Wikipedia claims that "The

glide ratio of paragliders ranges from 9.3 for recreational wings to about 11.3 for modern competition models,

[16] reaching in some cases up to 13.

[17] For comparison, a typical skydiving parachute will achieve about 3:1 glide. A hang glider ranges from 9.5 for recreational wings to about 16.5 for modern competition models. " Lets assume that we can make a steerable rocket drogue that has glide ratio g of 6: somewhere in between parachute and paraglider.

Lets assume that the rocket was downwind by a quarter of the altitude. D/H = 0.25.

Then to get the rocket to steer back we need at least Vf = (6/5.75) * Vw = 1.043 Vw. Vd = Vw/5.75 = 0.173 Vw.

How fast can a paraglider go? The same wikipedia link above says "The speed range of paragliders is typically 20–75 kilometres per hour (12–47 mph), from

stall speed to maximum speed. Beginner wings will be in the lower part of this range, high-performance wings in the upper part of the range.

[note 2] " Lets assume our drogue can go 30 mph.

Then the max wind speed we could tolerate would be 30/1.043 or 28.75 mph. The descent rate would be 5 mph. Put a rocket up 2.5 miles under these conditions and you will get it back in a half an hour. It would be really cool to watch.

I wonder if a better parachute/paraglider could be designed for this application that has a higher forward speed. It makes sense that people don't want to land too fast or they will break their legs.

Overall, it seems practical to use a steerable drogue chute with winds up to about 30 mph, which is not fast for high altitude. There could be some fun on a calm day flying up to maybe 15k' or so. I would love to watch a rocket come back for a half hour and land at the pad.