This entry was posted on April 30, 2014 by Bill Hansen.
Since the advent of inflatable traction kites, tube size is not only a constant question for designers but also for kiters of all disciplines. Tube size debates occasionally develop online and at the beach during discussions about performance of different styles and brands. Most kiters intuitively understand that bigger tubes are stiffer. They also understand that more pressure is needed to prevent buckling, particularly at the wingtips under higher loads. Some believe that bigger tubes create more powerful kites by increasing the kites foil (wing) profile.
Today, we're adding some clarity to the debate to move it to a more technical side.
WARNING: MATH AHEAD!
Tube Size and Deflection
For a basic cylindrical tube, the Moment (I) which is a measure of the distribution of material away from a central axis contributing to it's mechanical properties, is proportional to the Outside Diameter to the 4th power minus the Inside Diameter to the 4th power:
In the case of an inflatable kite's LE Tube, since it is a fabric cylinder with minimal mechanical properties other than tensile fiber strength, we will assume it to have zero inside diameter and uniformly filled with an unknown material.
For a loaded beam, the deflection for a given force is proportional to the length to the 3rd power divided by the moment.
The deflection is then proportional to:
Ultimately, we can view the LE Tube's deflection under load to be a function of length to the 3rd power divided by diameter to the 4th power. That is, given the same load, longer tubes deflect more than shorter ones and fatter tubes deflect less than thinner ones.
In the case of an inflatable kite's LE Tube, since it is a fabric cylinder with minimal mechanical properties other than tensile fiber strength, we will assume it to have zero inside diameter and uniformly filled with an unknown material.For a loaded beam, the deflection for a given force is proportional to the length to the 3rd power divided by the moment.The deflection is then proportional to:Ultimately, we can view the LE Tube's deflection under load to be a function of length to the 3rd power divided by diameter to the 4th power. That is, given the same load, longer tubes deflect more than shorter ones and fatter tubes deflect less than thinner ones.
Example 1: A 10% longer tube would deflect 33% more
Example 2: A 10% Fatter tube would deflect 32% less
Example 2: A 10% Fatter tube would deflect 32% less
But how do these relationships apply to a kite? Let's imagine a 10 sqm flat rectangular outline inflatable kite with a 10cm diameter 5m straight Leading Edge Tube and 2m center strut hard-lined at the wigtips. If the span is increased 10% (Aspect ratio increased 21%) theoretically we would need to increase the LE Tube Diameter roughly 10% to compensate. The new kite would need to have an 11cm LE Tube 5.5m long with a center strut length of 1.82m.
Pumping Pressure
But what about pumping pressure? It has been shown that the buckling mechanism for inflated beams is similar to plasticity failure in solid beams. That is the fiber stress in the wall of the tube due to the inflated pressure goes to zero at the moment of buckling. In the case of our flat kite, the tube will start to buckle when the compression due to loading exceeds the tension from pumping pressure along the lower side of the tube. In this case the buckling load can be shown to be proportional to the pressure times the diameter to the 3rd power divided by the length.
In simple terms, for a given kite, the force needed to cause a tube to buckle is directly proportional to the pumping pressure. It is also very dependent on diameter such that even slightly bigger tubes are much less likely to buckle at the same pressure. Clearly pumping a kite with a long unsupported wingtip or a small leading edge tube to a higher pressure will help preserve the shape.
In simple terms, for a given kite, the force needed to cause a tube to buckle is directly proportional to the pumping pressure. It is also very dependent on diameter such that even slightly bigger tubes are much less likely to buckle at the same pressure. Clearly pumping a kite with a long unsupported wingtip or a small leading edge tube to a higher pressure will help preserve the shape.Leading Edge Tube Drag
The aerodynamic drag of a cylinder normal to the flow is proportional to the 'frontal area' which is Length times the Diameter and varies with the Velocity squared.
Looking at frontal area alone, our higher aspect example kite will have 21% higher drag due to the larger (11cm diameter) and longer (5.5m) leading edge. However, this clearly is a simplistic calculation because it ignores the other contributors to overall drag such as profile shape and induced drag considerations for a higher aspect design. The question becomes more whether the LE tube diameter is sufficient to support the load and not buckle for an average pumping pressure.
Looking at frontal area alone, our higher aspect example kite will have 21% higher drag due to the larger (11cm diameter) and longer (5.5m) leading edge. However, this clearly is a simplistic calculation because it ignores the other contributors to overall drag such as profile shape and induced drag considerations for a higher aspect design. The question becomes more whether the LE tube diameter is sufficient to support the load and not buckle for an average pumping pressure.Leading Edge Diameter and Profile
The wing profile (shape in the direction of airflow) for inflatable kites is generally a circle combined to a tangential cambered plate. For theoretical examination, we have four profiles of 12% max thickness at 25% of chord.
While it is often thought that larger Leading Edge Tubes contribute to power, it is obvious that they limit the associated canopy curve behind them as opposed to a 100% cambered membrane with no tube. The more likely cause of the perception of 'power' due to a larger leading edge is the increased drag which contributes to pull in the lines and sitting back in the window with a higher angle of attack.
While it is often thought that larger Leading Edge Tubes contribute to power, it is obvious that they limit the associated canopy curve behind them as opposed to a 100% cambered membrane with no tube. The more likely cause of the perception of 'power' due to a larger leading edge is the increased drag which contributes to pull in the lines and sitting back in the window with a higher angle of attack.
Results
For a Leading Edge Diameter of 14cm, increasing by 5% to 14.7cm and by 10% to 15.4cm would have the following effects.
For a Leading Edge Diameter of 14cm, increasing by 5% to 14.7cm and by 10% to 15.4cm would have the following effects.
Optimizing Leading Edge Diameter
The most difficult task is optimizing the diameter such that it is just small enough to support the dynamic lifting and bridle loads without buckling under normal pumping pressures and use. The optimal tube will vary substantially between kites of different outline, profile, use and construction (such as segmented or constant curve.) Kites with extremely small tubes tend to be very responsive and fast but lack power in turns due to excessive twisting and can fold during water re-launch. Kites with excessively large tubes tend to be slow and have higher turning bar pressure because they are overly stiff. They can also be hard to water re-launch.
By perusing the local beach, it is pretty obvious that some kites have relatively larger tubes. The question is are they engineered to be optimal for structure or performance?
By perusing the local beach, it is pretty obvious that some kites have relatively larger tubes. The question is are they engineered to be optimal for structure or performance?
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