Ballistic trajectory computer

Claim 1

A system for determining the ballistic range in an exponential atmosphere of a weapon having a known initial velocity at a known altitude above a target said system comprising: a clock generator for generating clock pulses; first computing means an exponential factor relating air density at a given altitude to that at a standard pressure plane; second computing means responsive to said pulses from said clock generator for solving in real time the simultaneous non-linear differential ballistic equations as a point by point trajectory of said weapon from said known altitude to said target, the range and altitude values defining said trajectory being calculated at times determined by said clock pulses, said second computing means further including means for employing re-computed values of said exponential factor as the computed value of altitude of said weapon decreases from said given altitude to the altitude of said target; and means for terminating operation of said second computing means when the most recent value of altitude calculated by said second computing means equals that of said target, whereby said ballistic range is determined by the corresponding calculated range value.

Claim 2

A system for determining the ballistic range in an exponential atmosphere of a weapon having a known initial velocity at a known altitude above a target said system comprising: a clock generator for generating clock pulses; first computing means an exponential factor relating air density at a given altitude to that at a standard pressure plane; second computing means responsive to said pulses from said clock generator for solving in real time the simultaneous non-linear differential ballistic equations as a point by point trajectory of said weapon from said known altitude to said target, the range and altitude values defining said trajectory being calculated at times determined by said clock pulses, said second computing means further including means for employing re-computed values of said exponential factor as the computed value of altitude of said weapon decreases from said given altitude to the altitude of said target; and means for terminating operation of said second computing means when the most recent value of altitude calculated by said second computing means equals that of said target, whereby said ballistic range is determined by the corresponding calculated range value.

Claim 5

A system for computing range X of a weapon along a ballistic trajecTory from a higher first altitude to a lower, second altitude as a function of time from integration of simultaneous non-linear differential equations, said system comprising: first means for developing a first term including an exponential factor as function of altitude; second means for developing a second term equal to the square root of the sum of the square of vertical and horizontal velocities; third means for formulating the product of said first and second terms, and for formulating horizontal and vertical acceleration values from products of respective horizontal and vertical velocities with said product; fourth means for digitally integrating said values of horizontal and vertical accelerations by generating increments of change in horizontally and vertical velocity as a function of time and by accumulating said increments of change in velocity to provide new values of horizontal and vertical velocities; fifth means for causing said third means to formulate a new horizontal acceleration value for each new value of horizontal velocity provided by said fourth means, and to formulate a new vertical acceleration value for each new value of vertical velocity provided by said fourth means; and sixth means for digitally integrating said new values of horizontal and vertical velocities by generating increments of change in horizontal and vertical position as a function of time and by accumulating said increments of change in position to provide new values of range and altitude position, whereby said range X is given by the value of range corresponding to the altitude value equal to that of the target.

Claim 6

A system for computing range X of a weapon along a ballistic trajecTory from a higher first altitude to a lower, second altitude as a function of time from integration of simultaneous non-linear differential equations, said system comprising: first means for developing a first term including an exponential factor as function of altitude; second means for developing a second term equal to the square root of the sum of the square of vertical and horizontal velocities; third means for formulating the product of said first and second terms, and for formulating horizontal and vertical acceleration values from products of respective horizontal and vertical velocities with said product; fourth means for digitally integrating said values of horizontal and vertical accelerations by generating increments of change in horizontally and vertical velocity as a function of time and by accumulating said increments of change in velocity to provide new values of horizontal and vertical velocities; fifth means for causing said third means to formulate a new horizontal acceleration value for each new value of horizontal velocity provided by said fourth means, and to formulate a new vertical acceleration value for each new value of vertical velocity provided by said fourth means; and sixth means for digitally integrating said new values of horizontal and vertical velocities by generating increments of change in horizontal and vertical position as a function of time and by accumulating said increments of change in position to provide new values of range and altitude position, whereby said range X is given by the value of range corresponding to the altitude value equal to that of the target.

Claim 9

A system for determining ballistic range and time of fall of a weapon having a given initial velocity at a given altitude above a target said system comprising: a clock pulse generator; first means responsive to said clock pulses for generating by digital integration instaneous values of vertical velocity, vertical velocity squared and increments of altitude change above said target from instantaneous values of vertical acceleration; second means responsive to said clock pulses for generating by digital integration instantaneous values of horizontal velocity, horizontal velocity squared and range from instantaneous values of horizontal acceleration; third means responsive to said first and second means for continually developing by digital servo the square root of the sum of said vertical velocity squared and said horizontal velocity squared; fourth means for continually developing an instantaneous value of an exponential of the form KBe Y/b in response to said increments of altitude change, where all except Y are constants and Y is the instantaneous value of altitude above said target; and fifth means for developing new instantaneous values of horizontal and vertical acceleration in accordance with said equations of motion whenever a selected one of said exponential, said vertical velocity, and said horizontal velocity changes value sixth means for storing a value equal to said altitude above said target, and for decreasing the stored value of altitude as said first means determines increments of altitude change to provide an instantaneous value of altitude Above said target; and a counter for counting the number of pulses generated by said clock pulse generator; whereby said ballistic range and time of fall are provided by the instantaneous values provided by said second means and said counter respectively when said sixth means provides a zero value for altitude above target.

Claim 10

A system for determining ballistic range and time of fall of a weapon having a given initial velocity at a given altitude above a target said system comprising: a clock pulse generator; first means responsive to said clock pulses for generating by digital integration instaneous values of vertical velocity, vertical velocity squared and increments of altitude change above said target from instantaneous values of vertical acceleration; second means responsive to said clock pulses for generating by digital integration instantaneous values of horizontal velocity, horizontal velocity squared and range from instantaneous values of horizontal acceleration; third means responsive to said first and second means for continually developing by digital servo the square root of the sum of said vertical velocity squared and said horizontal velocity squared; fourth means for continually developing an instantaneous value of an exponential of the form KBe Y/b in response to said increments of altitude change, where all except Y are constants and Y is the instantaneous value of altitude above said target; and fifth means for developing new instantaneous values of horizontal and vertical acceleration in accordance with said equations of motion whenever a selected one of said exponential, said vertical velocity, and said horizontal velocity changes value sixth means for storing a value equal to said altitude above said target, and for decreasing the stored value of altitude as said first means determines increments of altitude change to provide an instantaneous value of altitude Above said target; and a counter for counting the number of pulses generated by said clock pulse generator; whereby said ballistic range and time of fall are provided by the instantaneous values provided by said second means and said counter respectively when said sixth means provides a zero value for altitude above target.

Claim 12

A system for determining time of fall of a weapon from a known altitude above target comprising: means for generating clock pulses; computing means responsive to pulses from said clock means for solving in real time simultaneous non-linear differential equations of motion by integration to obtain corresponding values of altitude and range as a function of real time starting from said known altitude employing an exponential term for the value of air density which increases exponentially from an initial value at said known altitude as said weapon falls; exponential generating means for developing the initial value of said exponential term at said known altitude; and a counter for counting said clock pulses during the operation of said computing means whereby time of fall is given by said counter when said computing means indicates an altitude equal to that of the target.

Claim 13

A system for determining time of fall of a weapon from a known altitude above target comprising: means for generating clock pulses; computing means responsive to pulses from said clock means for solving in real time simultaneous non-linear differential equations of motion by integration to obtain corresponding values of altitude and range as a function of real time starting from said known altitude employing an exponential term for the value of air density which increases exponentially from an initial value at said known altitude as said weapon falls; exponential generating means for developing the initial value of said exponential term at said known altitude; and a counter for counting said clock pulses during the operation of said computing means whereby time of fall is given by said counter when said computing means indicates an altitude equal to that of the target.