To complete:
Excerpts:
2. Literature review 2.1 Drag Analysis
Drag analysis is a weak function of the speed of descent and decreases exponentially at higher velocities, influenced by a combination of factors, including the Reynolds number at high speeds and changes to the canopy during high speeds.
Conclusion : […] as canopy size increased, both drag coefficient and stability increased substantially.
But it seems that small parachutes are studied in this publication. See “Fig 4.2.1 Graph of drag coefficient against canopy size from CFD”, diameter from 65.2 cm to 85.2 cm. Things could be different at high scales.
I will try to see the behavior of larger parachute kites and with different relative or absolute wind speeds.
To start, some sources of rescue parachutes indicates the respective sink rates for a same parachute with the maximum load and with a lower load, leading to a higher Cd with a lower load:
Page 6:
technical specifications
Area ----------------------------------- 31.75m2
Weight -------------------------------- 1,620gr
Height lines --------------------------- 493cm
No. of panels -------------------------- 7/2
Maximum load EN / LTF ---------------- 115kg
Holomogation ------------------------- EN1249
Rate of fall under maximum load ------- 3.93m/s
Rate of fall under load of 90 k --------- 3m/s
My comment with unknowns concerning the precise L/D ratio according to the two different sink rates and corresponding loads: 31.75 m² or 35 m² (see the specifications below and which are a little different concerning the area of 35 m² or 39 m²), projected area 25 m² (?) if surface is 35 m², sink rate with 115 kg (1128.15 N): 3.93 m/s, horizontal speed 2.62 m/s with a glide ratio of 1/1.5, combined speed 4.7 m/s, elevation angle of 33°40’, leading to a thrust coefficient Ct of 3.4, a drag coefficient Cd of 2.84, a lift coefficient Cl of 1.89, similar to that on my publications about Rogallo and square rescues (Ct of 3.425, Cd of 2.86, and Cl of 1.9) that include the calculation details. That said a sink rate of 3.93 m/s is perhaps achieved with a slightly higher glide ratio than 1/1.5. Now, 3 m/s sink rate with 90 kg (882.9 N), leads to Ct = 4.56, Cd = 3.8, Cl = 2.53, horizontal speed 2 m/s.
max load (kg)|110|130|
surface (m²) |35.1|39|
My assessment may be completely inaccurate, but Cd variation is demonstrated and looks to increase linearly (not exponentially) with the decrease of the sink rate by a lower load: 3.93 m/s / 3 m/s = 1.31; the Cd of 2.84 at a sink rate of 3.93 m/s and a load of 115 kg becomes roughly 3.72 (the estimation being 3.8 in the calculation above) at a sink rate of 3 m/s and a load of 90 kg.
A similar observation can be done from the information on:
Another publication:
The publication entitled “EVOLUTION OF THE RINGSAIL PARACHUTE” could also be relevant for a preliminary assessment, because the high diameters of the studied parachutes can match the dimensions of the investigated AWES. The parachutes including only one chute on Table 1 have diameters from 29.6 ft to 189.6 ft for a drag coefficient Cd from 0.67 to 0.92 according to a slightly but almost consistent increase with both the increase of the diameter and the slight decrease of the nominal rate of descent.
The Cd (from 1.1 to 0.68 then 0.67) versus rate of descent (from 20 ft/sec to 35 ft/sec then 45 ft/sec) are reported on Fig. 17.
In the analyses and examples below the comparison can be a bit random because the parachutes can have different shape features.
The fourth parachute of 74.2 ft diameter and the eighth parachute of 136 ft diameter which includes three chutes, with Cd of 0.78 and 1.03 respectively for a nominal rate of descent barely different of 20.6 ft/sec and 20 ft/sec respectively. The ninth parachute of 156 ft diameter includes also three chutes, and has a Cd of 1.1, just like the tenth parachute also of 156 ft, but including six chutes.
Note that the seventh parachute with a single chute of 128.8 ft diameter, 27.9 ft/sec rate of descent and 0.749 lb/ft² load, has a Cd of 0.9 which is equivalent to that of 0.92 for the twelfth and final parachute with a single chute of 189.6 ft diameter, for a comparable rate of descent of 25.5 ft/sec, and for a comparable 0.708 lb/ft² load, and for a diameter far higher. In this example, and perhaps also of other parachutes of comparable large size (see the observation below), the size does not look to be an important parameter.
Now in the following two examples, I will try to see if we can deduce the Cd by equalizing the parameters as much as possible (notably lb/ft²), considering a linear increase in Cd with the increase in diameter, and a linear decrease in Cd with the increase in the rate of descent, and for the parachutes with only one chute.
From the (second in the table) parachute with Cd of 0.68, 41 ft diameter, 35 ft/sec rate of descent and 0.985 lb/ft² load, to the seventh with Cd of 0.9, 128.8 ft diameter, 27.9 ft/sec rate of descent and 0.749 lb/ft², the area being 9.8688 (about 10) times that of the 41 ft parachute. 41 ft/sec is 1.47 times 27.9 ft/sec. So, even by a linear increase in Cd with a decrease of the rate of descent, the Cd should become 0.68 x 1.47 = 1, then 1 x 3.14 / 0.985 x 0.749, so a Cd of about 2.39. This is far above the real value of 0.9. That doesn’t work!
Now the first two parachutes have an equivalent Cd (respectively 0.67 and 0.68), but the first one, 29.6 ft in diameter, and 1.577 lb/ft², has a significantly higher rate of descent of 55 ft/sec, against respectively 35 ft/sec (55² being roughly 35² x 2.47), 41 ft diameter (1.385 times more), 0.985 lb/ft². Our Cd of 0.67 should go to 0.68. 0.67 x 1.57 x 1.385 / 1.577 x 0.985 = Cd of 0.91. That doesn’t work, but is far closer to the reality (0.68).
Observation. For these two examples, we can remark that if we remove the increase of diameter as a parameter of increase of Cd, we achieve results that are close to the given values of Cd: 3.14 and 1.385 are respectively removed, leading to respective Cd of 1.1 (given Cd of 0.9) and Cd of 0.66 (given Cd of 0.67). Indeed, perhaps for large sizes, the variations of the diameter of the canopy could be neglected as shown in an example above.However, with the previous examples for the publication in reference (“EVOLUTION OF THE RINGSAIL PARACHUTE”), conclusions remain uncertain on the degree of increase in Cd when the speed of descent decreases.
In the case of linear decrease of Cd with the increase of the rate of descent (as partially shown on the specifications above) or wind speed, we will say that, for a Rogallo parachute kite drawn from a Rogallo rescue with a Cd let’s say 3 for a sink rate of 4 m/s (typical value), the Cd would become 1.5 with a wind speed of 8 m/s, and only 0.75 with a wind speed of 16 m/s.
But if we take into account the figures from tests (see below), it could be that the Cd decreases even faster when the wind speed increases.
| 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 |
With the same load of 13.78 lb and the same IFC-72-SUL parachute of 72 inches diameter, the Cd goes from 2.620 to 3.224, while the descent speed goes from 12.7 ft/sec (for a Cd of 2.62) to 11.45 ft/sec (for a Cd of 3.224). Globally the maximum descent speed variation is 10.91703 % increase, so about 11 %, while the maximum Cd variation is 23.05343 % decrease as deduced from Cd 3.224 / 2.62, so about 23%. Here the Cd decreases much faster than the descent speed increases. The Cd seems to decrease exponentially, following the increase of the square of the descent speed, at least compared to the two extreme values on this sample: 12.7² / 11.45² results in a variation of 23%, as for Cd 3.224 / 2.62 as noted above. See the quote given above, and which seems to apply:
The evaluations are complex and involve many parameters. But these elements do not seem to favor a possibility for a high Cd parachute kite in strong winds. Perhaps, but it is only a hypothesis, high Cd are more difficult to maintain in strong winds or high rates of descent.
The simpler would be testing any high Cd parachute (Rogallo or other) at different wind speeds and measuring the different values of the traction force.
