Tether drag lengthwise in a reeling system

I thing this has not been covered.

I was thinking about the tether drag on a reeling system. Lets assume a wind speed w. The reeling speed r is independent on w but looking towards experience with other designs, and related to tether strength, we can assume that r should be at least a third of w but more is better. The eact ratio is determined by a gearing ratio. For now lets assume the speeds are equal, r \approx w

The apparent airflow on the tether is thus increased to \sqrt{w^2 + r^2} and the tether drag is pointing in a 45 degree angle relative to the initial wing.

Anyways, the tether drag will be possibly quite significant acting as a «friction» force on the reeling system. The faster you reel, the more of this effect.

Lets also try with some numbers; assume a system with elevation angle 90 degrees producing 1 kW in 7 m/s wind, and also r =7. There are two tethers, due to reeling, and the distance ground to kite l is 200 m. Tether diameter d is 2 mm.

The drag on the tether lengthwise, as a loss to reeled power would be

D = \frac{1}{2} \rho \left[ 2 w^2 \right] d l 2 C_D \sin^2{\frac{\pi}{2}} \approx 7 \mathrm N

The power loss would thus be 0.07 kW, or close to 7% of the systems power output.

Following this thread about tether drag in reeling systems got me thinking.

To put it in everyday terms, it reminds me of a car antenna. When you’re driving fast, the antenna whips around in the wind? That’s kind of like the wind resistance on the tether.

Now, imagine you start retracting the antenna while you’re still driving fast. The antenna is fighting against the wind and the retraction force at the same time. That’s akin to the increased airflow on the tether when it’s being reeled in against the wind.

So, here’s the million-dollar question: How much energy does it take to retract the antenna against the wind? And is that anything like the power loss in a reeling system due to the tether drag?

The car antenna analogy might help to wrap our heads around the tether drag dynamics.

I think the calculation above should serve as a good initial guess. Also interesting in this analysis is that the tether drag itself increases.

But aero tether drag is complicated, I expect some numeric simulation could improve accuracy a lot.

Anyhow, I think the analysis so far shows that the effect is significant.

It is the same question.

The analogy of a car antenna retracting in the wind is a good way to understand the concept of tether drag in a reeling system. The antenna, like the tether, experiences a drag force due to the wind, and this force increases as the antenna is retracted (or as the tether is reeled in).

The energy required to retract the antenna against the wind can be thought of as the work done against the drag force. In this case, the force is the drag force on the antenna, and the distance is the length of the antenna that is retracted.

The power loss in the reeling system due to tether drag can be calculated in a similar way. The drag force on the tether is given by the equation:

D = 1/2 * ρ * w^2 * d * l * C_D * sin^2(π/2)

where:

  • D is the drag force,
  • ρ is the air density,
  • w is the wind speed,
  • d is the tether diameter,
  • l is the tether length, and
  • C_D is the drag coefficient.

The power loss due to this drag force is then given by D * r, where r is the reeling speed. This is analogous to the energy required to retract the car antenna against the wind.

So, in both cases, we are dealing with a drag force that increases with the speed of retraction (or reeling in), and this leads to an energy loss or power loss in the system. The exact values will depend on the specific parameters of the system (like the wind speed, tether diameter, reeling speed, etc.), but the underlying physics is the same.

Let’s calculate the power loss due to tether drag using the given parameters:

  • Wind speed (w) = 7 m/s
  • Reeling speed (r) = 7 m/s
  • Tether length (l) = 200 m
  • Tether diameter (d) = 2 mm
  • Drag coefficient (C_D) = 1 (assuming a worst-case scenario)
  • Air density (ρ) = 1.225 kg/m³ (at sea level and at 15 °C)

We can use Wolfram to perform this calculation.

The power loss due to tether drag in the reeling system, given the parameters provided, is approximately 84.035 Watts or 0.084 kW. This represents about 8.4% of the system’s power output of 1 kW.

This calculation is analogous to the energy required to retract a car antenna against the wind. The exact value in the car antenna case would depend on the specific parameters of the antenna and the wind speed, but the underlying physics is the same: a force (the drag force) is acting over a distance (the length of the antenna or tether), leading to an energy loss or power loss in the system.

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Thinking about this further, the whole thing makes me think of a balloon on a windy day. If you were pulling it in, the altitude would drop, right? The amount of tether catching the wind would go down too. Same with kites. That angled tether is actually kind of a perk since you’re exposing less of it to the wind, making it easier to reel in. I reckon it’s something to keep an eye on, but not losing sleep over it

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