www.PSFmagazine.com | March-April 2020 | 15 14 | March-April 2020 | Powered Sport Flying Light Sport Aircraft TECHTALK “Power Index Explored More Deeply” by Roy Beisswenger The FAA is loath to have prescriptive weight limits in MOSAIC. Instead, they are working with other kinds of formulae to describe limits without specifically calling out the actual weight of the aircraft. One idea floated within the FAA was to use a calculation called a Power Index or Ip. It is described by the formula: Ip = {(W/S)/(W/P)} 1/3, where: W = maximum takeoff weight (MTOW) in pounds, S = wing area in square feet, P = maximum rated power in horsepower at sea level and standard temperature. If the Ip value worked out to be less than 1.2, it was proposed at one point that the aircraft would fit within the definition of a Light Sport Aircraft. This formula would only work for airplanes, not applying to rotorcraft, powered parachutes and weight shift control trikes. Earlier, an Excel spreadsheet escaped from the FAA that allowed a user to plug in different values for maximum gross weight, wing area, and maximum horsepower and it would instantly calculate the Power Index value. Industry people played around with the spreadsheet, putting in different values. Soon they found that no matter what value they put in for the weight of an aircraft, it never changed the Ip. This became a topic of vigorous discussion. However, there is a very simple explanation for the lack of sensitivity of the formula to weight. And in fact, the explanation comes from algebraically simplifying the equation itself. When you do that, you find that even though weight appears in the original equation, it quickly drops out since it is in both the numerator and the denominator. So let’s start with the original equation: Ip = {(W/S)/(W/P)} 1/3 If you divide by a fraction, that means that you are multiplying by the inverse of that fraction. (The inverse meaning that you switch the numerator and denominator.) Doing that, you get this: Ip = {(W/S) * (P/W)} 1/3 That means that the weight is being divided by the weight, which works out to 1. The equation then solves to: Ip = {P/S} 1/3 That means that weight has no influence on the Power Index. Instead, the power index is essentially a ratio between the power of the engine in horsepower and the size of the wing. Now that the equation is simplified, we can do something else interesting. Let’s solve for Max Power: Ip = {P/S} 1/3 Ip³ = P/S Ip³ * S = P In other words, the larger the wing, the more power you can use. That certainly makes sense from a safety point of view. Solving for Max Wing Size: S = P/Ip³ That says the same thing. The more power you have, the larger your wings need to be. Let’s see what that looks like with some real world numbers. If you have a 100-hp motor (for example, the very common 100-hp Rotax 912uls) then for an Ip of 1.2, your smallest possible wing size is: S = 100/1.4³ = 57.87 square feet As an example, the wing area of a Flight Design ctsw is 107.0 square feet, indicating that it is considerably larger than the minimum 57.87 square feet defined by an Ip of 1.2. This probably means that an Ip of 1.2 is unlikely to be the only way that a light sport airplane will be defined with MOSAIC. Perhaps a smaller number will be used or perhaps it is only going to be one way of defining a light sport airplane (see above constraints). Perhaps a minimum stall speed (above) may also be included. That way a maximum gross weight won’t be cooked directly into the regulations, but will still end up being a consideration for airplane designers. The Flight Design CTLS is a light sport aircraft under the FAA current rules and would fit easily in the definition of a light sport aircraft under MOSAIC using the power index value proposed. In addition to the Power Index concept, here are methods to describe and constrain unlimited weight as learned in lama’s last conference with faa: • 200 horsepower hard point —As with other parts, this is not fully determined yet but 200 horsepower may be a cap • 50 knot stall — presumably with lift devices; such as flaps or leading edge devices deployed • 1.2 Power Index (still being devised; please do not assume this is a final value faa will accept for rule making) — See “tech talk” in the panel to the left. • Thus, aircraft that fit the criteria will likely weigh less than 3,000 pounds (≈1365 kilograms) This report is current and was reviewed in March 2020. It is as accurate as we can make it at this time, but it bears repeating one more time: this is a regulation still in process. Many changes may occur. Despite that caveat, the report shows where faa is generally headed with mosaic. Keep your seat belts fastened! Support Our Advertisers
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