High drag coefficient

Hey - how about a drag-based windmill??? :slight_smile:

The video and diagrams show a projected area a little less than half (about (\frac {2}{3})^2) of the flat area, which if sink rate was all due to drag, would result in more than doubling of the Cd, so a Cd of over 5, which is more than double than that of any object I am aware of, so there must be a mistake somewhere.

Terminal velocity: V_t=\sqrt{\dfrac{2mg}{\rho AC_d}}, rearranging for the unknowns: AC_d=\dfrac{2mg}{V_t^2\rho}. Inputting the known values for the middle parachute: AC_d=\dfrac{2\cdot101\cdot9.8}{(5.2)^2\cdot1.2}=60. Assuming sink rate is all due to drag and Cd is 2.5 gives you a projected area of 60/2.5=24m^2, which is more than double the given projected area.

Perhaps it is interesting to look at sink rates and drag coefficients of different parachutes a bit more.

I bet buoyancy plays a role, and lift in other types of parachutes.

In the end of my comment above I referred to the rescue parachute Yeti UL, S(19), mentioning that the video indicates a flat area of also 19 m² at 0:07. I am linking again this video (from the manufacturer Gin Gliders):

So at 0:07 seconds from the beginning, you can see the mention: Yeti UL flat area 19 m² and other specifications. I guess that flat area = projected area. So the whole area of the parachute is higher than 19 m². Otherwise the projected area would be still more tiny, leading to an unrealistically high drag coefficient.

That said the website specifies for the same model Yeti UL: S(19) Surface area (m²) 19 without specifying whether it is the flat area. We see a bit of curvature (much less than for other parachutes, hence its better sink rate for an equivalent whole surface) and above all almost vertical edges which add surface. So I think 19 m² is the flat area as specified on the video.

There are certainly things we don’t know about how to increase the drag coefficient, such as airflow or various aerodynamic effects.

Apart from this some training-chutes are used for sports (link from Joe Faust):

A little more effort, a little lift for the high drag coefficient parachute(s), and you get a reeling AWES with one or more very large surfaces…

At 0:08 in that video if you look down you see the two squares for each parachute, the smaller one is the projected area, the bigger the flat area. If you also look here Yeti UL - Planar rescue parachute | Gin Gliders on the table, it says surface area, which is equal to the given flat area. Also a bit lower down:

So flat area = surface area. Because the projected area is relatively larger you can get away with a lower surface area to get an equal projected area and so a lower weight and packing volume of the parachute.

1 Like

Indeed I just saw: “the two squares for each parachute, the smaller one is the projected area, the bigger the flat area”. And if you enlarge the video capture, you can read for the first parachute (Yeti UL), flat area (pointing to the bigger red square), projected area (pointing to the smaller dotted square); and for the second parachute (conventional rescue), difference between flat and projected area, with a smaller dotted square of the same dimensions (?) but a much bigger red square.

I also get approximately 5 for the Yeti UL (the planar rescue) by roughly estimating the projected area (a little more than half of 19 m², so about 10 m²) and counting the squares on top, of which there are 25, those on the edges being slanted, plus the vertical rectangles forming the edges around the perimeter.

The other parachutes in the range have a larger surface area for the same projected area, so the drag coefficient would be approximately the same at 5.

5 is an incredibly high value that seems impossible, and at the same time these parachutes seem to be incredibly small compared to their respective users.

I wanted to know more by asking the manufacturer with a mail: he indicated that some of the data is not in the public domain. I assume that to get a Cd of 5 (if it is the correct value), a lot of aerodynamic work had to be done.

I think that for a reeling (reel-in / out = yo-yo) AWES such surfaces could perhaps have an interest if a little lift allows them not to touch the ground, and knowing that high altitude winds would be approached by enlarging the surfaces (just as for traditional wind turbines that reach higher altitudes as they grow) or by stacking them.

Apart from that, I just tested one of these parachutes below, getting about 6 N with a more or less 2 m/s wind, then getting a maximum thrust of 20 N (I will try later with stronger winds and an anemometer) by trotting against this wind. Specifications on:
https://www.amazon.fr/dp/B07XGJCB7F?psc=1&ref=ppx_yo2ov_dt_b_product_details
I think 57 inches x 57 inches (1.45 m x 1.45 m) as shown on a photo, perhaps would lead to a projected area of about 2 m² which seems higher than the real projected area (1.5 m² ?). I measured its surface area at about 2.5 m².

See also the video about “Increasing Parachute Drag” (curve at 2:05, Descent Rate Comparison (Normal vs Reefed)) and the explains below:

A high drag coefficient (Cd) rescue parachute used as a yo-yo kite, flying at a low elevation angle, could look like this (Globe Light - Dudek) :

Or even (still lower elevation angle, but more vertical parachute (higher angle of attack):

Here the lift is only useful to prevent the kite from dragging on the ground or (for gigantic dimensions or by stacking parachutes) to avoid to catch people working on the site or to pull up trees. Even with a low angle of elevation, the parachute(s) can extend far enough to harness a large vertical frontal airspace including low and high altitude winds, a little like current wind turbines with their vertical rotors.

Besides that, we were talking about drag coefficients for rescue parachutes of maybe 5 for the square ones, and I would say a little less than 4 for the round ones, but without having the data, proceeding by more or less exact extrapolations.

But here is a table of drag coefficients for tested parachute recovery systems from
https://fruitychutes.com/help_for_parachutes/parachute-help/iris-parachute-cd-performance-log.htm

The table below shows our measurements done over a period of 5 years to accurately determine the coefficient of drag (Cd) of the Iris Ultra Parachutes.

All tests were done having measured the weight of the rocket accurately upon landing. In addition we had precise information on the parachutes themselves and used altimeters to log the data. Factors that affect the coefficient of drag are altitude, barometric pressure, air temperature, and humidity. The factors listed here, given that altitude stays constant, can vary the Cd by up to 20%. Fruity Chutes rating of 2.2 Cd is considered to be very close to the worst case that we had measured over many flights.

Fruity Chutes Iris Parachute Cd Performance Log

Rocket, Drone, or Company Who Chute Used Date Diameter (in) Recovery Weight Lbs Descent Fps Calculated Cd(frontal area)
Mag Max GE IFC-72 4/1/2011 72 15.53 15.05 2.103
Mag Max GE IFC-60 5/20/2011 60 16.1 17.9 2.219
Comp 4 GE IFC-72 5/21/2011 72 23.3 16.95 2.487
Mag Max GE IFC-72 6/12/2011 72 15.6 13.667 2.562
Comp 4 GE IFC-72 4/7/2012 72 22 18 2.083
Comp 4 GE IFC-72 5/19/2012 72 23.6 16.85 2.549
Comp 4 GE IFC-72 6/16/2012 72 23 16.75 2.514
Not sure DR IFC-60 7/20/2012 60 16.8 18.5 2.168
Max Maxx Thunderdome GE IFC-72-ZP 1/2/2016 72 19.025 13.97 2.990
MN Drone Ido IFC-66-SUL 1/22/2016 66 13.78 14.57 2.369
MN Drone Ido IFC-66-SUL 1/22/2016 66 13.78 12.66 3.138
MN Drone Ido IFC-66-SUL 1/22/2016 66 13.78 13.06 2.949
MN Drone Ido IFC-72-SUL 1/22/2016 72 13.78 12.7 2.620
MN Drone Ido IFC-72-SUL 1/22/2016 72 13.78 11.45 3.224
MN Drone Ido IFC-72-SUL 1/22/2016 72 13.78 12.57 2.675
MN Drone Ido IFC-72-SUL 1/22/2016 72 13.78 12.04 2.916
Mag Maxx Thunderdome GE IFC-72-ZP 2/6/2016 72 19.025 15.6 2.398

Average Cd 2.586

I noted a Cd of 3.224, and for drone recovery. The rescue parachutes for paraglider pilots mentioned earlier may have even higher requirements and seem to have a higher Cd.

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.

1 Like

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:

TECHNICAL SPECIFICATIONS

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):

https://iopscience.iop.org/article/10.1088/1742-6596/2230/1/012017
PDF:
Influence of angle-of-attack on drag force
AIXIANG Ma, SHIJIN Zhou, QIAN Wu and CHUANLEI Zhu

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:

https://web.wpi.edu/Pubs/E-project/Available/E-project-042407-112440/unrestricted/Brighenti_Duffen_Head_Vented_Parachutes_MQP.pdf

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

The new link (the old link is dead) on tested drag coefficients (Cd) is on Iris Ultra Parachute Cd Performance Log | Fruity Chutes.

I put again this excerpt:

Given that the altitude stays constant, the factors above can cause the Cd to vary by up to 20%. Fruity Chutes rating of 2.2 Cd is considered to be very close to the worst case that we had measured over many flights.

Indeed some measured values are impressive, such like 3.224.

In this thread a Cd of 5 was evoked, but this value is likely very exaggerated, some unknown such like the real (not maximum) load for the sink rate and the ratio between surface area and projected area are not fully known.

The Cd varied between approximately 2.1 and 3.2. As weather conditions and the possible presence of ascendants or descents could modify the Cd values, we could make an average which would give something like a Cd of 2.65.

On the video on a previous comment one can see that Cd is improved when the parachute center is pulled (reefed parachute to increase drag at 0:45).

The following parachute is in a good place for high Cd tested by Fruity Chutes:

We can see that there is a big central hole and this hole is pulled.

It is not impossible that this has the effect of reducing the projected surface, which would initially require more fabric for the same projected surface in order to benefit of a higher Cd, which remains to be verified.

Perhaps I could increase the Cd of this cheap parachute game by pulling the central hole (perhaps it would be better with a larger central hole). Actually I obtained a Cd above 1, but not far more.

Today I experimented the same parachute with a tiny pilot kite.

Parachute of projected area of about 5 m², with a small lifter kite of 0.2 m². This was too small to provide the parachute with a constant and significant angle of elevation. On the other hand, the parachute did not seem to have a tendency to rotate as when it is alone. The tether of the lifter kite was attached to the periphery of the central hole.

1 Like

Testing a 16ft Annular Parachute

Our Annular design is also the most efficient chute weight vs drag on the market

A simple way to make it fly like a kite? And then a depower device?

Link now: