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# Photos of the observed flyers and the tracking device. (A) A paragliding pilot and a bird of prey thermalling together. (B) Peregrine falcon with the GPS device on its back. (C) Schematic picture of the thermalling and gliding parts of the flights with the notations indicated.

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Gliding saves much energy, and to make large distances using only this form of flight represents a great challenge for both birds and people. The solution is to make use of the so-called thermals, which are localized, warmer regions in the atmosphere moving upwards with a speed exceeding the descent rate of bird and plane. Whereas birds use this te...

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... of the MacCready Theory. In this theory the relation between the horizontal and the corresponding sinking speeds (the so-called gliding polar curve, p(x), characteristic for the given gliding object) is used. It is supposed that the climbing rate of the next thermal is known by the flyer, and no geographical effects are taken into account. We apply the following interpretation of the MacCready theory. The goal of the gliders is to make a given distance L AB (using both thermalling and gliding and not loosing height in average) during a time as short as possible. Thus, they intend to minimize the quantity (time) L AB 1/v xy − v z /(v xy v climb ) , where v xy , v z = p(v xy ) are the gliding horizontal and vertical velocities, and v climb denotes the climbing rate in the thermals (see Fig. 1 and SI Appendix Fig. 2). The optimal strategy is determined from equalling the derivative of this expression to zero, and in this way obtaining a relationship between the optimal v xy and v climb . This leads to the expression p(v xy ) − v climb v xy = dp(v xy ) dv ...

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