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A system for the measurement of an angle of roll of a projectile is disclosed. The projectile has a casing with a rear end, a front end, and a side wall extending therebetween. The system includes a radar configured to transmit a polarized electromagnetic signal toward the projectile and a groove di

A system for the measurement of an angle of roll of a projectile is disclosed. The projectile has a casing with a rear end, a front end, and a side wall extending therebetween. The system includes a radar configured to transmit a polarized electromagnetic signal toward the projectile and a groove disposed on the side wall of the casing. The groove has a width, a depth, and a length, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the length extending along the outside of the casing. The radar is further configured to receive a return signal from the projectile, wherein the return signal from the groove is modulated as a function of the angle of roll of the projectile. Amplitude or phase modulation of the return signal from the groove can be used to uniquely determine the roll angle of the projectile.

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What is claimed is: 1. A projectile comprising: a casing with a rear end, a front end, and a side wall extending between the rear and front ends; and a roll-angle groove for tracking the roll angle of the projectile disposed on the side wall of the casing, the roll-angle groove having a width, a de

What is claimed is: 1. A projectile comprising: a casing with a rear end, a front end, and a side wall extending between the rear and front ends; and a roll-angle groove for tracking the roll angle of the projectile disposed on the side wall of the casing, the roll-angle groove having a width, a depth, and a length, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the length extending along the outside of the casing. 2. The projectile of claim 1, wherein the length of the roll-angle groove extends in a plane that is perpendicular to the longitudinal axis. 3. The projectile of claim 2, wherein the roll-angle groove further comprises a pair of opposed sides and a pair of opposed ends. 4. The projectile of claim 3, wherein the depth of the roll-angle groove is constant. 5. The projectile of claim 4, wherein the width of the roll-angle groove comprises a first width between the opposed sides at each of the opposed ends and a second width between the opposed sides at a center of the roll-angle groove. 6. The projectile of claim 5, wherein the second width is greater than the first width and the width of the roll-angle groove increases from each of the opposed ends to the center. 7. The projectile of claim 6, wherein a first opposed side is substantially perpendicular to the longitudinal axis and a second opposed side is in a plane that extends at an acute angle relative to the first opposed side such that the width of the roll-angle groove increases from each of the opposed ends to the center of the roll-angle groove. 8. The projectile of claim 6, wherein the increase in the width of the roll-angle groove is monotonic. 9. The projectile of claim 3, wherein the opposed sides are substantially parallel to each other such that the width of the roll-angle groove is constant between the opposed ends. 10. The projectile of claim 9, wherein the depth of the roll-angle groove further comprises a first depth at each of the opposed ends and a second depth at a center of the roll-angle groove. 11. The projectile of claim 10, wherein the second depth is greater than the first depth and the depth of the roll-angle groove increases from each of the opposed ends to the center. 12. The projectile of claim 11, wherein the increase in depth of the roll-angle groove is monotonic. 13. The projectile of claim 3, wherein the casing of the projectile is cylindrical at the location of the roll-angle groove. 14. The projectile of claim 3, wherein the length of the roll-angle groove is a complete thread along the outside of the casing that forms a thread groove. 15. A projectile comprising: a casing with a rear end, a front end, and a side wall extending between the rear and front ends; and a roll-angle groove for tracking the roll angle disposed on a cylindrical portion of the side wall of the casing, the roll-angle groove having a width, a depth, a first length, a pair of opposed sides and a pair of opposed ends, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the first length extending along the outside of the casing in a plane that is substantially perpendicular to the longitudinal axis, a deflecting groove disposed on the side wall of the casing, the deflecting groove having a second length along the outside of the casing, the first length of the roll-angle groove and the second length of the deflecting groove being capable of forming a substantially closed loop along the outside of the casing, wherein the length of the deflecting groove is disposed in a plane that has an acute angle off the latitudinal axis of the projectile. 16. The projectile of claim 15, further comprising a sectional groove formed at a point at which the front end is fixedly coupled to the side wall, the deflecting groove being disposed between the rear end of the projectile and the sectional groove, wherein the deflecting groove deflects the return signal of the sectional groove to facilitate reducing the interference of the return signal of the roll-angle groove. 17. A projectile comprising: a casing with a rear end, a front end, and a side wall extending between the rear and front ends; and a roll-angle groove for tracking the roll angle of the projectile disposed on the side wall of the casing of the projectile, the roll-angle groove having a width, a depth, a length, a pair of opposed sides and a pair of opposed ends, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the length extending along the outside of the casing configured substantially in the form of a thread groove substantially in a plane that is perpendicular to the longitudinal axis, wherein the opposed ends of the roll-angle groove are spaced apart a distance equal to along the longitudinal axis of the projectile, where λ is the wavelength of the transmitted radar signal and n is an integer. 18. A projectile comprising: a casing with a rear end, a front end, and a side wall extending between the rear and front ends; and a roll-angle groove for tracking the roll angle of the projectile disposed on the side wall of the casing of the projectile, the roll-angle groove having a width, a depth, a length, a pair of opposed sides and a pair of opposed ends, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the length extending along the outside of the casing configured substantially in the form of a thread groove substantially in a plane that is perpendicular to the longitudinal axis, wherein the opposed ends of the roll-angle groove are spaced apart a distance equal to along the longitudinal axis of the projectile for 0≦θ≦2π, where θ is the roll angle in radians, λ is the wavelength of the transmitted radar signal, and n is an integer. 19. A method of measuring an angle of roll of a projectile having a casing with a rear end, a front end, and a side wall therebetween, the method comprising: forming a roll-angle groove for tracking the roll angle of the projectile having a width, a depth, and a length on the side wall of the projectile, the width extending parallel to a longitudinal axis of the projectile, the depth extending inwardly from an exterior of the casing toward the longitudinal axis, and the length extending along the exterior of the casing perpendicularly to the width, the roll-angle groove having a pair of opposed sides and a pair of opposed ends; transmitting a polarized electromagnetic signal toward the projectile, the projectile having a radar signature that varies with the angle of roll of the projectile; receiving a return signal from the projectile, the return signal being modulated by at least a portion of the projectile on which the roll-angle groove is disposed; and processing the return signal to determine the effect of the roll-angle groove on the modulated return signal. 20. The method of claim 19, the forming step further comprising: forming a width of the roll-angle groove comprising a first width between opposed sides at each of the opposed ends and a second width between opposed sides at a center of the roll-angle groove; forming the second width to be greater than the first width such that the width of the roll-angle groove increases from each of the opposed ends to the center; forming one of the opposed sides to be substantially perpendicular to the longitudinal axis and the other of the opposed sides to be diagonal to the longitudinal axis such that the width of the roll-angle groove increases from each of the opposed ends to the center of the roll-angle groove; and forming the width of the groove to monotonically increase from each of the opposed ends to the center of the roll-angle groove. 21. The method of claim 19, wherein the length of the roll-angle groove comprises first and second halves, and the first half and the second half of the roll-angle groove are symmetrical. 22. The method of claim 19, the forming step further comprising: forming a first depth at each of the opposed ends and a second depth at a center of the roll-angle groove; forming the second depth to be greater than the first depth; forming the depth of the roll-angle groove to increase from each of the opposed ends to the center of the roll-angle groove; forming depth of the roll-angle groove to monotonically increase from the end of the opposed ends to the center of the roll-angle groove. 23. A method of measuring an angle of roll of a projectile having a casing with a rear end, a front end, and a side wall therebetween, the method comprising: forming a roll-angle groove on the side wall of the projectile for tracking the roll angle of the projectile, the roll-angle groove having a width, a depth, a length, a pair of opposed sides and a pair of opposed ends, the width extending parallel to a longitudinal axis of the projectile, the depth extending inwardly from an exterior of the casing toward the longitudinal axis, and the length extending perpendicularly to the width-having a first periphery along the outside of the casing; forming a sectional groove at a point at which the front end is coupled to the side wall; forming a deflecting groove that is disposed on the side wall of the casing between the rear-end of the projectile and the sectional groove, the deflecting groove having a length that has a second periphery along the outside of the casing located substantially in a plane that is diagonal to the longitudinal axis of the projectile, the first periphery of the roll-angle groove and the second periphery of the deflecting groove aligned in a substantially closed loop along the outside of the casing; transmitting a polarized electromagnetic signal toward the projectile, the projectile having a radar signature that varies with the angle of roll of the projectile; receiving a return signal from the projectile, the return signal being modulated by at least a portion of the projectile on which the roll-angle groove is disposed; and processing the return signal to determine the effect of the roll-angle groove on the modulated return signal. 24. A method of measuring an angle of roll of a projectile having a casing with a rear end, a front end, and a side wall therebetween, the method comprising: forming a roll-angle groove as a continuous thread along the outside of the casing to form a thread groove; the roll-angle groove having a width, a depth, a length, a pair of opposed sides and a pair of opposed ends; the width extending parallel to a longitudinal axis of the projectile, the depth extending inwardly from an exterior of the casing toward the longitudinal axis, the length extending along the exterior substantially perpendicular to the width, and the opposed ends being spaced apart by a distance equal to along the longitudinal axis of the projectile, where λ is the wavelength of the transmitted radar signal and n is an integer; transmitting a polarized electromagnetic signal toward the projectile, the projectile having a radar signature that varies with the angle of roll of the projectile; receiving a return signal from the projectile, the return signal being modulated by at least a portion of the projectile on which the roll-angle groove is disposed; and processing the return signal to determine the effect of the roll-angle groove on the modulated return signal. 25. A method of measuring an angle of roll of a projectile having a casing with a rear end, a front end, and a side wall therebetween, the method comprising: forming a roll-angle groove as a continuous thread along the outside of the casing to form a thread groove; the roll-angle groove having a width, a depth, a length, a pair of opposed sides and a pair of opposed ends; the width extending parallel to a longitudinal axis of the projectile, the depth extending inwardly from an exterior of the casing toward the longitudinal axis, the length extending along the exterior substantially perpendicular to the width, and the opposed ends being spaced apart by a distance equal to along the longitudinal axis of the projectile, for 0≦θ≦2π, where θ is the roll angle in radians, λ is the wavelength of the transmitted radar signal, and n is an integer; transmitting a polarized electromagnetic signal toward the projectile, the projectile having a radar signature that varies with the angle of roll of the projectile; receiving a return signal from the projectile, the return signal being modulated by at least a portion of the projectile on which the roll-angle groove is disposed; and processing the return signal to determine the effect of the roll-angle groove on the modulated return signal. 26. A system for the measurement of an angle of roll of a projectile, the system comprising: a projectile having a casing with a rear end, a front end, and a side wall extending between the rear and front ends, the projectile further having a roll-angle groove for tracking the roll-angle of the projectile disposed on a cylindrical portion of the side wall of the casing, the roll-angle groove having a width, a depth, and a length, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the length extending along the outside of the casing; radar configured to transmit a polarized electromagnetic signal toward the projectile and to receive a return signal from the projectile, the return signal being modulated as a function of the angle of roll of the projectile; and processing means for analyzing the modulated return signal, the processing means determining the angle of roll by determining a modulating effect of the roll-angle groove on the return signal. 27. The system of claim 26, wherein the roll-angle groove further comprises a pair of opposed sides and a pair of opposed ends, wherein the depth of the roll-angle groove is constant, wherein the width of the roll-angle groove comprises a first width at each of the opposed ends and a second width at a center of the roll-angle groove, the second width being greater than the first width and the width of the roll-angle groove increasing from each of the opposed ends to the center. 28. The system of claim 26, wherein the opposed sides are substantially parallel to each other such that the width of the roll-angle groove is constant between the opposed ends, wherein the depth of the roll-angle groove has a first depth at each of the opposed ends and a second depth at the center of the roll-angle groove, the second depth being greater than the first depth and the depth of the roll-angle groove increasing from each of the opposed ends to the center. 29. A system for the measurement of an angle of roll of a projectile, the system comprising: a projectile having a casing with a rear end, a front end, and a side wall extending between the rear and front ends, the projectile further having a roll-angle groove for tracking the roll angle of the projectile disposed on a cylindrical portion of the side wall of the casing, the roll-angle groove having a width, a depth, and a first length, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the first length extending along the outside of the casing; the projectile further comprises a deflecting groove disposed on the side wall of the casing, the deflecting groove having a second length along the outside of the casing, the first length of the roll-angle groove and the second length of the deflecting groove forming a substantially closed loop along the outside of the casing, wherein the deflecting groove extends substantially in a plane at an acute angle relative to the latitudinal axis of the projectile; radar configured to transmit a polarized electromagnetic signal toward the projectile and to receive a return signal from the projectile, the return signal being modulated as a function of the angle of roll of the projectile; and processing means for analyzing the modulated return signal, the processing means determining the angle of roll by determining a modulating effect of the roll-angle groove on the return signal. 30. A system for the measurement of an angle of roll of a projectile, the system comprising: a projectile having a casing with a rear end, a front end, and a side wall extending between the rear and front ends, the projectile further having a roll-angle groove is a continuous thread along the outside of a cylindrical portion of the side wall of the casing, the roll-angle groove having a width, a depth, and a length, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the length extending along the outside of the casing, the opposed ends of the roll-angle groove having a distance between each other, the distance being along the longitudinal axis of the projectile, where λ is the wavelength of the transmitted radar signal and n is an integer; radar configured to transmit a polarized electromagnetic signal toward the projectile and to receive a return signal from the projectile, the return signal being modulated as a function of the angle of roll of the projectile; and processing means for analyzing the modulated return signal, the processing means determining the angle of roll by determining a modulating effect of the roll-angle groove on the return signal. 31. A system for the measurement of an angle of roll of a projectile, the system comprising: a projectile having a casing with a rear end, a front end, and a side wall extending between the rear and front ends, the projectile further having a roll-angle groove is a continuous thread along the outside of a cylindrical portion of the side wall of the casing, the roll-angle groove having a width, a depth, and a length, the width extending along a longitudinal axis of the projectile, the depth extending inwardly from an outer surface of the casing toward the longitudinal axis, and the length extending along the outside of the casing, the opposed ends of the roll-angle groove having a distance between each other, the distance being along the longitudinal axis of the projectile for 0≦θ≦2π where θ is the roll angle in radians λ is the wavelength of the transmitted radar signal and n is an integer; radar configured to transmit a polarized electromagnetic signal toward the projectile and to receive a return signal from the projectile, the return signal being modulated as a function of the angle of roll of the projectile; and processing means for analyzing the modulated return signal, the processing means determining the angle of roll by determining a modulating effect of the roll-angle groove on the return signal. 32. A projectile comprising a casing with a rear end, a front end, a side wall, and a thruster for changing the direction of the projectile, the side wall comprising means for tracking the roll rate and roll angle of the projectile, the means for tracking comprising means for reflecting an electromagnetic signal such that the amplitude or phase of the reflected electromagnetic signal varies as a function of the angular orientation of the projectile; the thruster operating to steer the projectile to an intended target based upon the tracked roll angle and roll rate of the projectile. 33. The projectile of claim 32, wherein the means for reflecting an electromagnetic signal comprises a roll-angle groove.