Why Do Birds of Prey Fly in Circles? Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? Zs Akos et al. Proc. Natl. Acad. Sci. 105 4139-4143 (2008) Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? How long do they fly? Does that help find food? Zs Akos et al. Proc. Natl. Acad. Sci. 105 4139-4143 (2008) Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? How long do they fly? Does that help find food? They ride thermals - allowing them Zs Akos et al. Proc. Natl. Acad. to hunt longer with less energy. Sci. 105 4139-4143 (2008) Why should you care? Zs Akos et al. Bioinspir. Biomim. 5 045003 (2010) Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? How long do they fly? Does that help find food? They ride thermals - allowing them Zs Akos et al. Proc. Natl. Acad. to hunt longer with less energy. Sci. 105 4139-4143 (2008) Why should you care? Climate change? Zs Akos et al. Bioinspir. Biomim. 5 045003 (2010) Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? How long do they fly? Does that help find food? They ride thermals - allowing them Zs Akos et al. Proc. Natl. Acad. to hunt longer with less energy. Sci. 105 4139-4143 (2008) Why should you care? Climate change? Bird lovers? Zs Akos et al. Bioinspir. Biomim. 5 045003 (2010) Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? How long do they fly? Does that help find food? They ride thermals - allowing them Zs Akos et al. Proc. Natl. Acad. to hunt longer with less energy. Sci. 105 4139-4143 (2008) Why should you care? Climate change? Thermal soaring Bird lovers? flight of birds and UAVs Zs Akos et al. Bioinspir. Biomim. 5 045003 (2010) Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? How long do they fly? Does that help find food? They ride thermals - allowing them Zs Akos et al. Proc. Natl. Acad. to hunt longer with less energy. Sci. 105 4139-4143 (2008) Why should you care? Climate change? Thermal soaring Bird lovers? flight of birds and UAVs PRIVACY!! Zs Akos et al. Bioinspir. Biomim. 5 045003 (2010) Does the Eagle Make It? – p. 1/3
Why Do Birds of Prey Fly in Circles? To find food. But why circles and not straight lines? Do they actually do circles? How long do they fly? Does that help find food? They ride thermals - allowing them Zs Akos et al. Proc. Natl. Acad. to hunt longer with less energy. Sci. 105 4139-4143 (2008) Why should you care? Climate change? Thermal soaring Bird lovers? flight of birds and UAVs PRIVACY!! Zs Akos et al. Bioinspir. Biomim. Big increase in drones coming in 2015. 5 045003 (2010) Does the Eagle Make It? – p. 1/3
Riding the Thermals A bald eagle is flying near the James River in search of critters to eat. To stay aloft longer, it orbits in thermals. The eagle has a mass m e = 5 kg and can maintain a bank angle µ = 40 ◦ while it orbits (see figure) and a speed v e = 14 m/s . Its wings exert a lift force | � L | = 45 N perpendicular to its ve- locity and the plane of its wings. The ther- Top mal is cylindrical with a radius r t = 35 m view and exerts a vertical force of | � F t | = 12 N on the eagle. Can the eagle orbit in the thermal without losing altitude? Assume it r e attempts to fly horizontally. Does the Eagle Make It? – p. 2/3
Newton’s Laws 1. Consider a body with no net force acting on it. If it is at rest it will remain at rest. If it is moving with a constant velocity it will continue to move at that velocity. 2. For all the different forces acting on a body Σ � F i = m� a . 3. For every action there is an equal and opposite reaction. F AB = − � � F BA Does the Eagle Make It? – p. 3/3
Newton’s Laws - An Example Two blocks are connected by a rope draped over a pulley as shown below. The masses are m 1 = 1 . 0 kg and m 2 = 4 . 0 kg . What is the acceleration of both masses? m 1 m 2 Does the Eagle Make It? – p. 4/3
Combining Forces On A Falling Balloon A hot-air balloon of mass M is descend- ing vertically with a downward accelera- tion a as shown below. How much ballast m b must be thrown out to give the balloon the same magnitude acceleration in the opposite direction (up)? Assume the up- ward force of the hot air does not change as ballast is dropped and express your answer as an equation in M , a , and any necessary constants. Does the Eagle Make It? – p. 5/3
Force and Motion NOT constant acceleration!! Does the Eagle Make It? – p. 6/3
Force and Motion NOT constant acceleration!! Clean the tracks!! Does the Eagle Make It? – p. 6/3
Force and Motion Does the Eagle Make It? – p. 7/3
Force and Motion Does the Eagle Make It? – p. 8/3
Force and Motion Does the Eagle Make It? – p. 8/3
Riding the Thermals A bald eagle is flying near the James River in search of critters to eat. To stay aloft longer, it orbits in thermals. The eagle has a mass m e = 5 kg and can maintain a bank angle µ = 40 ◦ while it orbits (see figure) and a speed v e = 14 m/s . Its wings exert a lift force | � L | = 45 N perpendicular to its ve- locity and the plane of its wings. The ther- Top mal is cylindrical with a radius r t = 35 m view and exerts a vertical force of | � F t | = 12 N on the eagle. Can the eagle orbit in the thermal without losing altitude? Assume it r e attempts to fly horizontally. Does the Eagle Make It? – p. 9/3
Circular Motion - 1 Does the Eagle Make It? – p. 10/3
Circular Motion - 2 r y x origin Does the Eagle Make It? – p. 11/3
Circular Motion - 3 θ 1 θ 2 θ 0 /2 θ 0 /2 r 2 r 1 Does the Eagle Make It? – p. 12/3
Circular Motion - 3 v s ∆ 1 θ 1 θ 2 r ∆ θ 0 /2 θ 0 /2 v 2 r 2 r 1 Does the Eagle Make It? – p. 13/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ θ 0 /2 θ 0 /2 v 2 r 2 r 1 Does the Eagle Make It? – p. 14/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ r ∆ θ 0 /2 θ 0 /2 r 1 r 2 v 2 θ 0 r 2 r 1 v 2 θ /2 v ∆ 0 θ /2 0 v 1 Does the Eagle Make It? – p. 15/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ r ∆ θ 0 /2 θ 0 /2 r 1 r 2 v 2 θ 0 r 2 r 1 v 1 θ /2 v ∆ 0 θ /2 0 v 1 Does the Eagle Make It? – p. 16/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ r ∆ θ 0 /2 θ 0 /2 r 1 r 2 v 2 θ 0 r 2 r 1 v 1 θ /2 v ∆ 0 θ /2 0 v 2 Does the Eagle Make It? – p. 17/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ r ∆ θ 0 /2 θ 0 /2 r 1 r 2 v 2 θ 0 r 2 r 1 v 1 θ /2 v ∆ 0 θ /2 0 v 2 Does the Eagle Make It? – p. 18/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ r ∆ θ 0 /2 θ 0 /2 r 1 r 2 v 2 θ 0 r 2 r 1 v 1 θ /2 v ∆ 0 θ /2 0 v 2 Does the Eagle Make It? – p. 19/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ r ∆ θ 0 /2 θ 0 /2 r 1 r 2 v 2 θ 0 r 2 r 1 v 1 θ /2 v ∆ 0 θ /2 0 v 2 Does the Eagle Make It? – p. 20/3
Circular Motion - 3 v s ∆ 1 θ /2 0 θ 0 /2 r ∆ r ∆ θ 0 /2 θ 0 /2 r 1 r 2 v 2 θ 0 r 2 r 1 v 1 θ 0 v ∆ v 2 Does the Eagle Make It? – p. 21/3
Riding the Thermals A bald eagle is flying near the James River in search of critters to eat. To stay aloft longer, it orbits in thermals. The eagle has a mass m e = 5 kg and can maintain a bank angle µ = 40 ◦ while it orbits (see figure) and a speed v e = 14 m/s . Its wings exert a lift force | � L | = 45 N perpendicular to its ve- locity and the plane of its wings. The ther- Top mal is cylindrical with a radius r t = 35 m view and exerts a vertical force of | � F t | = 12 N on the eagle. Can the eagle orbit in the thermal without losing altitude? Assume it r e attempts to fly horizontally. Does the Eagle Make It? – p. 22/3
Does the Eagle Make It? 60 50 r e � m � net � N � � blue � 40 r t � m � 30 r e � m � � red � and F y 20 net � N � F y 10 0 � 10 0 10 20 30 40 50 Μ � deg � Does the Eagle Make It? – p. 23/3
Does the Eagle Make It? 60 50 r e � m � net � N � � blue � 40 r t � m � 30 r e � m � � red � and F y 20 net � N � F y 10 0 � 10 0 10 20 30 40 50 Μ � deg � Does the Eagle Make It? – p. 24/3
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