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I have a kayak and a bike. I routinely put them on top of my car and drive 60-70 mph for hundreds of miles. I am curious how much this affects my gas mileage.

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The best way: just do it. Go out and drive on the highway for some distance with the kayak and bike on top of your car, and measure the amount of fuel used, then do the same trip without the items on top of your car and measure the amount of fuel used in that case. The trip would have to be long enough that you can get a fairly accurate measurement of how much fuel you used.

What you could do is fill up your fuel tank immediately before setting out each time, then fill it up again when you get back, and the amount of gas you need to buy will tell you how much you used. Just make sure to use the same gas station, and preferably the same pump, for every measurement.

If you want to calculate it theoretically, that's a whole different story. Presumably the kayak and bike on top of your car increase the drag force and thus reduce its fuel efficiency, but as far as I know there's no way to do a calculation without a complex aerodynamic simulation.

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Ah, an empirical approach! Very nice. –  Jen May 17 '11 at 20:00
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In practice it is not easy to do. If you have different wind conditions for the two runs that could make a large difference. Also drag increases with velocity, so you would have to keep the same speed for both runs (not easy with a lot of traffic). –  Omega Centauri May 17 '11 at 20:04
    
True, ideally you'd do this several times and take an average. –  David Z May 17 '11 at 20:07
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There are two things that get affected by the roof items. One is the frontal area of the car, and the second is the coefficient of drag for the car.

There is no rule of thumb, but in order to estimate the combined effect, then drive up to 60mph, put the car in neutral and measure how long it takes to coast down to like 50mph. Then try again with stuff on your roof. If time decreases $X$% then you can estimate that the rolling resistance increases by $X$% also, and hence your consumption goes up. Note that it makes sense to use a very flat road, and use measurements in both directions in negate the wind effects. If you average 3-5 measurements per direction you will get a good idea of the effect of the roof stuff.

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You can also calculate drag from terminal velocity if you have a convenient cliff. It is recommended that you repeat the experiment a few times for an accurate result –  Martin Beckett May 17 '11 at 20:35
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