High drag coefficient

I haven’t seen a reasoning for doing this that takes into account the supposed lower power available. Let’s say fixed wing flying crosswind has a TSR of 7 and this 0.7, that gives you a 2 orders of magnitude difference in power achievable?

And let’s say the wind speed varies from 1 to 7, what wind speed are you sizing your generator for and can it handle wind speeds outside of that? Can your parachute? Etc. etc.

This topic is about high drag coefficient. Yo-yo mode is described in numerous topics, so it can be easy to know why a high Cd could be interesting, and why I mentioned it, although such an application is not the main object of this topic.

However, the many substantive errors in the previous message lead me to clarify some points already made. First of all it is obvious that what is dealt with here takes place in tether-aligned category as for Guangdong parachute HAWP, not in crosswind category: see the AWES classification which clearly distinguishes these two categories. See also Tethered-aligned vs crosswind kites in yo-yo mode

There is no TSR (tip speed ratio) for tether-aligned AWES, and in this case no “this 0.7”.

In addition, the reel-out speed of the tether depends on the wind speed, not the (crosswind) kite speed, and is conventionally set at 1/3, although it can vary significantly. As a result, the characteristics of the generator will not change fundamentally between using a fast crosswind kite and a tether-aligned device.

Guangdong HAWP describes how their tether-aligned parachute device works: their description is available on Zhonglu High Altitude Wind Power Technology - 中路高空风力发电技术 - #2 by PierreB.
See the section “Parachute Aerodynamics” page 10 and following pages whose the first equation page 14.

The main point to consider is what is called the “tangential force T (along the axe)” (page 10) which is the vector sum of the drag and lift. The coefficient provided on page 11 varies between 0.6 and 1.2.

When I started this topic, I was surprised to see 2.2 Cd, having noticed later that much larger Cd exist: tested Cd of 3.224, perhaps Cd of 5 for some rescue parachutes.

Assuming our Cd of 5 parachute is about 100 m², at 12 m/s wind speed and an air density of 1.2, we would have a power of 76.8 kW (force x reel-out speed of 1/3 wind speed, taking into account the loss caused by the decrease in apparent wind) during reel-out phase.This is not far from half of the average 92 kW tested with a soft wing of equivalent or even larger size and flying crosswind, and by maximizing Power to space use ratio while simplifying steering, not to mention rigid wings which, assuming a positive average power in reeling mode, deviate still more from this important ratio.

Of course, the parachute kite could not fly strictly horizontally (hence the illustrations in my previous post) and would have to have a minimum angle of elevation: at this stage, I don’t know what its Cd would be and also its Cl, hence its tangential force.

But the existence of very high Cd gives food for thought for AWES in yo-yo mode and capable of scaling up to any dimensions, stacking them if necessary.

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I use TSR incorrectly to refer to kite:wind speed ratio. I don’t see other mistakes in my short comment. The only positive statement that gives you a 2 orders of magnitude difference in power achievable? is also phrased as a question to invite a reasoned refute.

The question is about accommodating different wind speeds, not reeling speeds. For a wind speed of 7 vs. 1 you would need to have a generator that could handle 50 times the power, and you would need a parachute and tethers 50 times stronger. With something flying crosswind you just need to fly a different pattern.

I would assume there was some mistake before believing an unremarkable shape achieved double the drag coefficient NASA for example was able to achieve. It needs more verification anyway.

On your three points.

1). Indeed, the explanation of point 2) clarifies your previous comment. On the substance, the “2 orders of magnitude difference in achievable power” are based on the surface area of the respective two kites, not their respective masses at equivalent wind power, let alone the power/space use ratio.

2). True, this is an advantage for crosswind kites, although a strong enough parachute could be made in order to work up to high winds, and then partially de-powered by deformation using some of the suspension lines when the winds are too fast. As far as generators are concerned, the problem is perhaps not so different from that of other flying devices.

3). I had even stayed at a drag coefficient of 1 or 1.2. NASA provides (on the following link) a drag coefficient (Cd) of 1.75 for parachute for recovery on Velocity During Recovery . That said a Cd of 3.224 have been tested according to Iris Parachute for an equivalent product.

And you yourself pointed out to me that when the calculation was based on the projected area (which I didn’t initially), the Cd was 5, which I also deducted. You thought it was a mistake, and I had a hard time believing it myself.

I asked the manufacturer for the Cd of their rescue parachutes, without success. I saw that no manufacturer mentions complete specification including both projected area and Cd.

Now, one only has to look at these parachutes to see that they are tiny compared to those of yesteryear. So there has been progress on that: you can now put a parachute in your pocket, which was unthinkable a short time ago. And the information given has little risk of being false for such sharp products: you can’t cheat on the sink rate. As for the shape, if you look closely, you can see a network of straps or ropes integrated into the canopy, which can influence the shape and lead to an increase in the Cd. We already know that bringing back the top of a parachute increases the Cd somewhat (see Increasing Parachute Drag - YouTube).

One thing would be to test a new (or otherwise disused) rescue parachute against the wind and measure the force and wind speed at the same time.

ChatGPT says:

NASA seems to confirm this in the link you also found: Velocity During Recovery and this video calls it canopy area. Another link: fluid dynamics - Reference area of a parachute - Physics Stack Exchange

So, one mistake was to use the projected area instead of the planform/canopy area in the calculation.

The planform area, as described above looks to be the surface area. I used the given surface areas in my first calculations:


SIZE S (19) M (23) L (27)
Surface area (m2) 19 23 27
Weight (kg) 0.87 0.99 1.17
Packed volume (cm3) 2025 2475 3006
Sink rate (m/s) 5.3 5.2 5.1
Maximum load (kg) 85 100 120
Certification EN 12491:2015 EN 12491:2015 EN 12491:2015

Drag coefficients become XXL: 2.65 for S (19), 2.68 for M (23), 2.85 for L (27) if I am right.

You replied:

It is known, and this is even truer for some square parachutes, that the projected area is much smaller than the surface area.

There is a contradiction by writing …as you need the projected area (from the quote just above), then

By dint of contradicting others, one ends up contradicting oneself…

Some use the projected area as reference area, like the calculator above, and others use the surface area, which significantly changes the Cd value.

As an example below:

Apparently NASA uses the “parachute area” (similar to surface area) as the reference area to determine the Cd (1.75), while Fruity Chutes seem to use the projected area in a similar way than the calculator above, which leads to higher values (about 1.6 or 1.7 times more):

Influence of angle-of-attack on drag force

An interesting article, see Fig.4 page 4 and explanations:

The simulation of the canopies with different angle-of-attack can calculate the drag coefficient directly, which helps to compare the parachute’s performance in the oblique airdrop.

Another relevant publication for the topic:

See table 5 page 61, and Figures 34-38 pages 62-64.