Peter Lynn ARCHIVE
Summary
The following report outlines a method for the testing of kites Lift to Drag ratio. To perform the test the flyer simple has to fly the kite in a horizontal circle while walking directly away from the kite. The Lift to Drag ratio is effectively the ratio of the Line length to the circle radius walked. The method requires some adjustment due to mass effects and line drag. It also requires the flyer to walk directly away from the kite and in the case of four line kites for the back line tension to be constant for the results to be accurate. However, the basic method provides a quick and cheap method for kite flyers to determine the performance of their kites.
Introduction
Determining the LTD of Kites is becoming increasingly necessary as the market for traction kites gets larger and more demanding. To test kites Canterbury University in Christchurch New Zealand in conjunction with Peter Lynn Kites LTD have been developing a kite test rig. At present the rig is mounted on the top of a car the kite flown above it. The kites line pull and line angle data are collected using a data acquisition system at a range of speeds. This data is then analysed to determine kite performance. Various methods have been developed to verify the results that have been obtained. The following article outlines a method that is thought to be the easiest determination of kites lift to drag ratio that currently exist.
What is the lift to drag ratio and why is it important.
The lift to drag ratio of a kite is defined as the forces perpendicular to the apparent wind (Lift) divided by the forces parallel to the apparent wind (Drag). Therefor the LTD ratio is
LTD = Lift/Drag = (CL*.5*density*Area*Velocity2 - Mass*Gravity)/CD*.5*density*Area*Velocity2
If the kite is flying directly above the flyer this ratio is related to the line angle with the ground by the formula
Tan(line angle)=LTD
The ratio is important because it determines the pointing ability of the kite in kitesailing/surfing/buggying applications and the maximum speed that can be obtained. The maximum speed is determined by the formula
Vehicle Velocity = True Wind Velocity * LTD
How to do the test
Go to a beach with your chosen kite on a day with no wind. Measure the length of the lines that you have including the bridle length. Fly the kite in a horizontal circle around you by walking directly away from the kite. By the time that you have flown the kite in a full circle you will have also walked in a complete circle. Measure the radius of the circle that you have made in the sand. The LTD of you kite can then be approximated by the following formula.
LTD = (R2 + (L+BL)2)1/2/R
where R= radius of the circle walked
L= Length of the lines used
BL = bridle length
Outline of the theory.
Figure 1 is a diagram indicating all the main forces that are acting on this system. The lift force acts perpendicular to the apparent wind and the drag force acts to the apparent wind. The resultant force provides a combination of line tension and a driving force which moves the kite. Naturally for a kite to complete the circle the driving force must never pulling the kite backwards. This can only happen if the relative wind direction enables the resultant force to be pointing in with or slightly in front of the line direction.
If the kite were to be flown in a circle without the flyer moving the apparent wind would be tangential to the circle and because nothing in this world has a LTD of infinity the kite will move backwards (see figure 2). However, if the flyer moves backwards in the direction of the kite line the apparent wind angle will be greater and there is now the possibility for a positive driving force (see figure 3). Due to Newtons laws the kite will accelerate until the resultant force is once again parallel with the line. This speed is the fastest that the kite can fly at and therefor determines the LTD. Because the velocity is a ratio f the distance that the kite must ly to the distance that the flyer must walk it does not matter how fast the flyer walks away from the kite the circle that they walk in will not be any bigger (in fact it will make some difference - see section xx). Only if the line length is changed will the radius change. Figure 4 shows how equation 1 is obtained.
Errors in method
There are a number of difficulties that induce errors into the determination of errors.
Kite Mass
The actual LTD of a kite is dependent on the mass of the kite. Usually, the formula for LTD is formula 1. With the kite been flown near to the horizontal part of the lift force must be used to lift the kite of the ground. The formula for LTD becomes
LTD = ((CL.0.5.density.A.V2)2 -mg2)1/2/ CD.0.5.density.A.V2
This is a slight difference but is perhaps a better reflection of the LTD of kite how they are actually flown. However, the true LTD can still be determined with a little more work. If the time taken to complete the circle is determined and varied between runs then the flying velocity can be determined by the fomula
Velocity = distance/time = (R2 + (L+BL)2)1/2/time
Applying the value of velocity to formula xx through trial and error the CL/CD or the aerodynamic LTD can then be determined.
Line Drag
Line and bridle drag plays a significant role in the performance of a kite. Unfortunately, when using this method the velocity of the air over the line is varying as you get further away from the kite flyer. Therefor the lines do not experience the same amount of drag along its length. This happen in real life anyway because kites are flow in the boundary layer but a boundary layer is parabolic in shape (approx a 1/7 power law) whereas this is a linear relationship. The line drag is likely to be less. Table 1 shows the adjustment factors that can be applied to the to the calculation to get a more accurate line drag effect.
Walking angle.
It is very important that the flyer walks directly away from the kite. If they do not they will stuff up the results. Probably the best way to get around this is to do about 10 circles. This has two benefits, firstly the average of the diameters will give you more reliable results and secondly by the time the flyer has waled ten circle in the sand they will start to get tired and begin walking in the most efficient way possible. The most efficient circle is to walk directly away from the kite.
Break Line Load
This method will work automatically for two-line kites where the LTD ratio cannot be adjusted by applying back line load. However, for four-line kites the back line load can be adjusted and this affects the results than can be obtained from this test as it is more than likely that the flyer will apply various amounts of back line tension. One way to counter this is to determine what percentage backline load is wanted to be tested. If handles are used a line can be attached to each handle at the appropriate distance along each handle an then the kite can be flown as a two line kite. The distances are determined by the formula.
Attachment point from front lines =back line load percentage/100*handle length
Test Results
To calibrate the test rig a 3.2 c-quad, a Peter Lynn Kite, has been used as the standard kite in all the runs. With 5% back line load the LTD of the kite is found to be 5.4+- 5%. Tests using the above method have obtained average results of 5.2.
Andy Ried, 2002(?)
