Slide #1.

Body Head Hemisphere Body Cylinder Tail Cone     Leg 1 Segment 1 Segment 2 Segment 3     Leg 2 Segment 1 Segment 2 Segment 3     Leg 3 Segment 1 Segment 2 Segment 3       Perimeter* Water Strider Body Segment Dimensions Radius Length Contact Perimeter (mm) (mm) (mm) 0.55 ----0.55 6.4 --0.55 2.6 --      Volume (mm3) 0.348 6.082 0.824   0.08 0.04 0.02   1.5 1.5 1.0   ----2   0.030 0.008 0.001   0.08 0.04 0.02   4.5 4.5 3.0   ----6   0.090 0.023 0.004   3.0 3.0 2.0 ----4 0.015 0.004 0.003 24       7.61 0.009132 0.04 0.02 0.02 Total Contact Total Volume** Body Mass (g) *Contact perimeter for Legs 1, 2, & 3 must be multiplied by 2 to account for the legs on either side of the body. **Total volume must include the volume of the body and the volume of the legs multiplied by 2 to
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Slide #2.

Math & Nature   Water striders ◦ Given 3) Find the ratio of body weight to surface tension force for the water strider.
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Slide #3.

Water Strider Body Segment Dimensions x 2 Radius Length Contact Perimeter Body (mm) (mm) (mm) Head Hemisphere 1.1 ----Body Cylinder 1.1 12.8 --Tail Cone 1.1 5.2 --          Leg 1 Segment 1 0.16 3.0 --Segment 2 0.08 3.0 --Segment 3 0.04 2.0 4           Leg 2 Segment 1 0.16 9.0 --Segment 2 0.08 9.0 --Segment 3 0.04 6.0 12           Leg 3 Segment 1 0.08 6.0 --Segment 2 0.04 6.0 --Segment 3 0.04 4.0 8 Total Contact   48 Perimeter*   Total Volume**     Body Mass (g)   Volume (mm3) 2.788 48.657 6.589   0.241 0.060 0.010   0.724 0.181 0.030   0.121 0.030 0.020   60.868 0.0730416 *Contact perimeter for Legs 1, 2, & 3 must be multiplied by 2 to account for the legs on either side of the body. **Total volume must include the volume of the body and the volume of the legs multiplied by 2 to
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Slide #4.

Water Strider Body Segment Dimensions x 4 Radius Length Contact Perimeter Body (mm) (mm) (mm) Head Hemisphere 2.2 ----Body Cylinder 2.2 25.6 --Tail Cone 2.2 10.4 --          Leg 1 Segment 1 0.32 6 --Segment 2 0.16 6 --Segment 3 0.08 4 8           Leg 2 Segment 1 0.32 18 --Segment 2 0.16 18 --Segment 3 0.08 12 24           Leg 3 Segment 1 0.16 12 --Segment 2 0.08 12 --Segment 3 0.08 8 16 Total Contact   96 Perimeter*   Total Volume**     Body Mass (g)   Volume (mm3) 22.301 389.256 52.712   1.930 0.483 0.080   5.791 1.448 0.241   0.965 0.241 0.161   486.949 0.5843388 *Contact perimeter for Legs 1, 2, & 3 must be multiplied by 2 to account for the legs on either side of the body. **Total volume must include the volume of the body and the volume of the legs multiplied by 2 to
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Slide #5.

Water Strider Body Segment Dimensions x 8 Radius Length Contact Perimeter Body (mm) (mm) (mm) Head Hemisphere 4.4 ----Body Cylinder 4.4 51.2 --Tail Cone 4.4 20.8 --          Leg 1 Segment 1 0.64 12 --Segment 2 0.32 12 --Segment 3 0.16 8 16           Leg 2 Segment 1 0.64 36 --Segment 2 0.32 36 --Segment 3 0.16 24 48           Leg 3 Segment 1 0.32 24 --Segment 2 0.16 24 --Segment 3 0.16 16 32 Total Contact   192 Perimeter*   Total Volume**     Body Mass (g)   Volume (mm3) 178.409 3114.047 421.694   15.442 3.860 0.643   46.325 11.581 1.930   7.721 1.930 1.287   3895.588 4.6747056 *Contact perimeter for Legs 1, 2, & 3 must be multiplied by 2 to account for the legs on either side of the body. **Total volume must include the volume of the body and the volume of the legs multiplied by 2 to
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Slide #6.

Math & Nature   Water striders 4) How big can a water strider get and still stay afloat?  At 2X  At 4X  At 8X
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