Doing the math from Kathryn's summary:
17 gallons at EWE (per fuel gauge)
Less 1.5 gallon per measured gauge error
= 15.5 potential gallons on board
Fuel burn:
1.2 hours at 100%, 7.1 gph (POH limited to 5 min) = 8.52 gal
Additional 0.4 hours in power mode, assume 7.0 gph = 2.8 gal
0.8 hours economy mode, 4.8 gph = 3.84 gal
2.4 hour flight to PWK, 15.2 gallons fuel needed.
Looks like using POH numbers and basic math wins again, within rounding error.
Perhaps someone planned the flight in economy mode, then flew mostly at full rental power to PWK??
The airplane's pilot operating handbook (POH) contains a flight limitation for a maximum continuous engine speed of 5,500 rpm. The POH also limits engine operation at 5,800 rpm to 5 minutes or less. The POH provides expected fuel consumption rates from sea level to 12,000 ft pressure altitude at engine speeds between 4,000 rpm and 5,500 rpm. According to the cruise performance tables, the expected fuel consumption rate at a cruise altitude of 3,000 ft and an engine speed of 5,500 rpm, with a standard temperature lapse rate, was about 5 gallons per hour. The POH does not provide fuel consumption rates for engine operations above 5,500 rpm.
The operator's manual for the Rotax 912iS engine states that the engine operates between two modes, economy and power, which have significantly different fuel consumption rates. The manual notes that the switchover between the economy and power modes occurs when the throttle position is advanced above 97%. In the economy mode, the expected fuel consumption rate was about 4.8 gallons per hour at 5,500 rpm and a manifold pressure of 27 inches of mercury. In the power mode, the expected fuel consumption rate was about 6.9 and 7.1 gallons per hour at 5,500 rpm and 5,800 rpm, respectively.
The airplane was equipped with a digital data module that recorded basic GPS, engine, and flight parameters. According to the recovered data, the airplane departed runway 3 at EYE and proceeded north-northwest toward PWK. A preliminary review of the available parameter data indicated that the flight from EYE to PWK was 2.3 hours at a cruise altitude of about 3,000 ft mean sea level (msl) and an engine manifold pressure of 26.5 to 27 inches of mercury. The engine data indicated that 60.4% of the flight, about 1.4 hours, was operated above 5,500 rpm. Additionally, the data indicated that about 74.6% of the flight, about 1.7 hours, was with the throttle positioned at or above 97% (where the engine normally switches between economy and power modes). The data indicated that about 52.5% of the flight, about 1.2 hours, was with the throttle positioned at 100%. Additionally, the engine had operated in power mode for 68.4% of the flight, about 1.6 hours
A postaccident examination of the airplane revealed that the fuel tank did not contain any useable fuel and the low fuel annunciator light was illuminated. Water was added to the fuel tank in 1 gallon increments to verify the accuracy of the fuel quantity gauge. The test results indicated that the low fuel light turned off after 1.75 gallons of water was added to the fuel tank. Additionally, the test results indicated that the fuel quantity gauge indicated on average about 1 to 1.5 gallons higher than the actual tank quantity.