I posted this on our Forum ( Wild Extremes) after a question about uphill/downhill shooting was asked and thought I'd post here if anyone was interested in it.
Understanding Arrow Trajectory
The slower the speed of a projectilethe more it will drop over the course of its flight. To compensate for this dropa projectile must be fired in an arched path to successfully strike the intended target. The arrow starts below the archer's line of sightrises above itand then drops back to his line of sight at the target. This curve in an arrow's path between bow and target is known as trajectory.
Trajectory is a crucial concern in bowhunting because a bowhunter simply can't escape its effects. People who contend that modern bows are so fast they're almost like rifles simply don't understand trajectory. Trajectory is directly related to the speed of a projectileand the very fastest bows shoot about 300 feet per second (fps) compared to the fast rifle at 3,000 fps. An arrow fired from such a bow has a greater trajectory over 30 yards than does a rifle bullet over 300 yards.
Instinctive shooters who must visualize the path of their arrows to the target know the importance of trajectory. But sight shooters with an understanding of trajectory find it easier to make good sight settings and are better able to avoid branches and other obstacles. And to accurately shoot uphill and downhillan understanding of trajectory is essential.
Visualizing Trajectory
Hitting obstacles ranks as one of the major reasons for missed shotsespecially for hunters pursuing whitetail deer and other forest animals. A clear understanding of trajectory can help you prevent many of these misses.
Firstremember that an arrow starts below your line of sight-as much as 6 inches or more if you're a release-aid shooter with a low anchor point. When your line of sight is well above an obstaclethere is a tendency to assume the arrow will clear with no problem. But because the arrow remains below your line of sight until it is 4 to 5 yards away from the bowit can slam into a nearby obstacle if you don't elevate high enough. Many hunters have blown easy shots by hitting stumpsrocks and other objects directly in front of them.
Learn to visualize arrow trajectory so you can cleanly shoot under or over limbs and other obstacles. It's possibleof courseto compute trajectory mathematicallybut it's not necessarily practical and may not help you in the field. Some simple steps on the target range will help you actually see the trajectory of your arrows.
Make sure your bow is sighted in at regular intervalssuch as 203040 and 50 yards. To determine the trajectory of your arrows at the halfway markyou'll be shooting target groups for each sight pin from a distance equal to half their sighted distance. Firststand 10 yards from the target and aim at the bullseye with your 20-yard pin. Shoot several groupsmeasuring the distance of each arrow above the center of the target; then average these numbers. This average is your midrange trajectory at 20 yards.
Shoot additional groups at 15 yards with your 30-yard pin; 20 yards with your 40-yard pin; 25 yards with your 50-yard pin. With increasing distanceyou'll find that your arrows hit progressively highergiving you a clear picture of the trajectory at each distance. For a bow shooting about 220 feet per second (fps)the midrange trajectory at 20 yards will be roughly 3 inches; at 30 yards6 inches; at 40 yards12 inches; and at 50 yards20 inches. At higher arrow speedsthe trajectory will be less; at slower speedsgreater. This method doesn't give peak trajectorieswhich are slightly closer to the targetbut it does give you a practical picture of midrange trajectory.
How do you put this knowledge to practical use? Let's assume you've drawn a bead on a buck standing 30 yards awayand there is a tree limb hanging in your path 15 yards outdirectly in the sight path between your bowsight and the deer's chest. An archer with no knowledge of trajectory might believe he has to maneuver to shoot either above and below the branchbut from your range test experienceyou know that your arrow will be 6 inches above your line of sight at the midway point in its flight. Fire away; your arrow will clear the branch cleanly. Similarlyif the offending branch is 6 inches or so above the sight linemany hunters would shootunaware that the arrow is likely to strike the branch. Youhoweverwill seek a new shooting positionlooking for a sight line which ensures that the arrow's midpoint trajectory is a safe distance away from the tree branch.
Remember also that when a sight pin rests on an object at the same distance as the sighted distance of the pinthe arrow will likely hit the object. Imaginefor examplethat you've put a pin on a deer 30 yards away using your 30-yard pin. But your 20-yard pin falls on a limb about 20 yards away. Your shot will miss the deerand the arrow will hit the limb.
Sight Window
At any given distanceyou have some leeway when estimating rangeand this leeway is called a sight window. Understanding the sight windows for your bow can help with shot selection. Againthe best way to learn about sight windows is by thorough practice-range work.
To gauge the window for your 20-yard sight pinfor exampleshoot at an 8-inch targetwhich is roughly the size of a large deer's kill zone when it is standing broadside. Start at 20 yardsand move closer1 yard at a timealways aiming at the center of the target with your 20-yard pin. The arrows will gradually move up until they begin hitting above the 8-inch target. That's the minimum end of your sight window. Now start again at 20 yardsand move back1 yard at a timeuntil your arrows hit below the circle. That's the maximum end of your sight window.
Repeat this test for each sight pin; for the 30-yard pinstart at 30 yards; for the 40-yard pinstart at 40 yards; and so forth. Move from the starting point toward the minimum end of each sight window; then move back from the starting point to determine the maximum end. The sight windows will become proportionately shorter as you move to the pins sighted for longer distancesdue to the increasing arc of the trajectory.
Shooting on an Angle
Bows are generally sighted in for horizontal shotswhere arrow trajectories are predictable. Howeverwhen you shoot from a high tree stand or on an uphill or downhill slopethe rules for trajectory change.
At a given distancegravity has the greatest effect on trajectory for an arrow flying horizontallyand has gradually less effect as the shooting angle is raised or lowered. The reason for this is that the trajectory arc is determined by the horizontal distance the arrow travelsnot the overall distance. When shooting at steep angleseither up or downaiming for the actual distance to the target is a mistakesince this measurement may be considerably larger than the horizontal distance that governs the arrow's trajectory. For exampleif you shoot at a target 40 yards away down a steep hillusing your 40-yard sight pinyour shot will probably go high of the mark. At steep anglesyou must learn to compensate by aiming low.
Contrary to common opinionthis principle applies equally to uphill and downhill shots. It's true that uphill trajectory begins to differ from downhill trajectory at some pointbecause gravity slows an arrow flying up faster than one flying down. But within standard hunting distances-50 yards and less-the difference is not significant. For practical purposesthenslant range can be computed identicallywhether the slope is uphill or down.
The trickof courseis determining how low to aim at different distances and slope angles. You can calculate this information geometricallybut to do so requires a calculatorelectronic rangefinderclinometer for measuring the angle of slopes and a good head for mathematics.
If you choose the mathematical methodyou can simplify this work by using a chart like the example shown here. A complete chart for all practical shooting distances will help you make clean kills at steep angles. To put such a chart to practical usehoweveryou must know the distance to the target and angle of slope. Steep slopes make range estimation difficult at bestso a good rangefinder can help here. With practice you can learn to estimate slope visuallyor you can buy a compass with a built-in clinometer to measure slope. Oryou can buy an expensive forester's clinometerwhich measures angle of slope precisely.
To be honestusing mathematics to calculate shooting adjustments is not very practical for most hunters. In the fieldgame animals rarely give you enough time to make the measurements and computationsand few hunters are enthused by the prospect of carrying a rangefindercalculator and printed charts into the field.
Most shooters find that simple practice gives them a feel for how upward and downward angles affect arrow trajectory. You can practice by shooting from a tree stand set to different heightsfor example. At each heightshoot several groups at varying distances from your stand.
Reducing Trajectory
Flattening the trajectory of an arrow reduces the need for precise range estimationstreamlines the process for shooting over and under obstacles and simplifies adjustments needed when shooting at upward and downward angles. Several factors-fletching arrow weight and air density-can affect trajectorybut arrow speed has the single greatest influence. For this reasonmanufacturers and archers continually seek ways to make their bows faster and faster.
You can increase arrow speed in several ways. One method is to reduce arrow weight. Each 5-grain reduction in arrow weight provides a speed increase of about 1 foot per second (fps). Thusif you reduce arrow weight by 100 grainsyou increase speed by roughly 20 fps.
Arrow speed can also be gained by increasing the draw weight of the bow. A 1-pound increase in draw weight yields an increase of about 2 fps in speed. Thus if you crank draw weight up by 10 poundsyou gain 20 fps in arrow speed.
Finallyshooting a bow with harder cams can increase speed. At a given draw weighthard cams can provide 10 to 20 percent more speed than round wheels.
Up to a pointspeed is good. But remember that the faster the arrowthe more "critically" it shoots. That isfaster arrows are more susceptible to uncontrolled oscillations and are more difficult to shoot with accuracy. At some pointthe loss in accuracy and consistency that comes with ultrafast arrows may negate any gains you get from the flattened trajectory. Faster arrows also make it harder to tune the bowespecially when the arrows are equipped with broadheads.
Rememberaccuracy is the number-one ingredient in clean kills. Lightning-fast arrows do you no good if they don't consistently hit the target.
Using Geometry to Calculate Arrow Trajectory
Here's how geometry can be used to calculate how arrow trajectory changes when shooting on an incline:
Visualize the hunting situation as a right-angle trianglewith two perpendicular legs; (A)the distance from the hunter to the ground; and (B)the distance from the animal to the ground directly below the hunter. The sloped hypotenuse(C)is the distance from the hunter to the animal. In essencethe drop of an arrow fired along the inclined hypotenuse will equal the drop of an arrow traveling the horizontal distance (B).
For exampleimagine you're on a cliffwhere you spot a buck standing below at a 45-degree angle to your line of sight. Your rangefinder shows that the distance along the sloped line to the buck is 30 yards. Using a basic formula from geometrycalled the Pythagorean Theorem (A2 + B2 = C2)you can calculate that side Brepresenting the horizontal distance to the deeris roughly 21 yards. To hit the deer in the kill zonethenyou would use the 20-yard sight pinnot the 30-yard pin.
Understanding Arrow Trajectory
The slower the speed of a projectilethe more it will drop over the course of its flight. To compensate for this dropa projectile must be fired in an arched path to successfully strike the intended target. The arrow starts below the archer's line of sightrises above itand then drops back to his line of sight at the target. This curve in an arrow's path between bow and target is known as trajectory.
Trajectory is a crucial concern in bowhunting because a bowhunter simply can't escape its effects. People who contend that modern bows are so fast they're almost like rifles simply don't understand trajectory. Trajectory is directly related to the speed of a projectileand the very fastest bows shoot about 300 feet per second (fps) compared to the fast rifle at 3,000 fps. An arrow fired from such a bow has a greater trajectory over 30 yards than does a rifle bullet over 300 yards.
Instinctive shooters who must visualize the path of their arrows to the target know the importance of trajectory. But sight shooters with an understanding of trajectory find it easier to make good sight settings and are better able to avoid branches and other obstacles. And to accurately shoot uphill and downhillan understanding of trajectory is essential.
Visualizing Trajectory
Hitting obstacles ranks as one of the major reasons for missed shotsespecially for hunters pursuing whitetail deer and other forest animals. A clear understanding of trajectory can help you prevent many of these misses.
Firstremember that an arrow starts below your line of sight-as much as 6 inches or more if you're a release-aid shooter with a low anchor point. When your line of sight is well above an obstaclethere is a tendency to assume the arrow will clear with no problem. But because the arrow remains below your line of sight until it is 4 to 5 yards away from the bowit can slam into a nearby obstacle if you don't elevate high enough. Many hunters have blown easy shots by hitting stumpsrocks and other objects directly in front of them.
Learn to visualize arrow trajectory so you can cleanly shoot under or over limbs and other obstacles. It's possibleof courseto compute trajectory mathematicallybut it's not necessarily practical and may not help you in the field. Some simple steps on the target range will help you actually see the trajectory of your arrows.
Make sure your bow is sighted in at regular intervalssuch as 203040 and 50 yards. To determine the trajectory of your arrows at the halfway markyou'll be shooting target groups for each sight pin from a distance equal to half their sighted distance. Firststand 10 yards from the target and aim at the bullseye with your 20-yard pin. Shoot several groupsmeasuring the distance of each arrow above the center of the target; then average these numbers. This average is your midrange trajectory at 20 yards.
Shoot additional groups at 15 yards with your 30-yard pin; 20 yards with your 40-yard pin; 25 yards with your 50-yard pin. With increasing distanceyou'll find that your arrows hit progressively highergiving you a clear picture of the trajectory at each distance. For a bow shooting about 220 feet per second (fps)the midrange trajectory at 20 yards will be roughly 3 inches; at 30 yards6 inches; at 40 yards12 inches; and at 50 yards20 inches. At higher arrow speedsthe trajectory will be less; at slower speedsgreater. This method doesn't give peak trajectorieswhich are slightly closer to the targetbut it does give you a practical picture of midrange trajectory.
How do you put this knowledge to practical use? Let's assume you've drawn a bead on a buck standing 30 yards awayand there is a tree limb hanging in your path 15 yards outdirectly in the sight path between your bowsight and the deer's chest. An archer with no knowledge of trajectory might believe he has to maneuver to shoot either above and below the branchbut from your range test experienceyou know that your arrow will be 6 inches above your line of sight at the midway point in its flight. Fire away; your arrow will clear the branch cleanly. Similarlyif the offending branch is 6 inches or so above the sight linemany hunters would shootunaware that the arrow is likely to strike the branch. Youhoweverwill seek a new shooting positionlooking for a sight line which ensures that the arrow's midpoint trajectory is a safe distance away from the tree branch.
Remember also that when a sight pin rests on an object at the same distance as the sighted distance of the pinthe arrow will likely hit the object. Imaginefor examplethat you've put a pin on a deer 30 yards away using your 30-yard pin. But your 20-yard pin falls on a limb about 20 yards away. Your shot will miss the deerand the arrow will hit the limb.
Sight Window
At any given distanceyou have some leeway when estimating rangeand this leeway is called a sight window. Understanding the sight windows for your bow can help with shot selection. Againthe best way to learn about sight windows is by thorough practice-range work.
To gauge the window for your 20-yard sight pinfor exampleshoot at an 8-inch targetwhich is roughly the size of a large deer's kill zone when it is standing broadside. Start at 20 yardsand move closer1 yard at a timealways aiming at the center of the target with your 20-yard pin. The arrows will gradually move up until they begin hitting above the 8-inch target. That's the minimum end of your sight window. Now start again at 20 yardsand move back1 yard at a timeuntil your arrows hit below the circle. That's the maximum end of your sight window.
Repeat this test for each sight pin; for the 30-yard pinstart at 30 yards; for the 40-yard pinstart at 40 yards; and so forth. Move from the starting point toward the minimum end of each sight window; then move back from the starting point to determine the maximum end. The sight windows will become proportionately shorter as you move to the pins sighted for longer distancesdue to the increasing arc of the trajectory.
Shooting on an Angle
Bows are generally sighted in for horizontal shotswhere arrow trajectories are predictable. Howeverwhen you shoot from a high tree stand or on an uphill or downhill slopethe rules for trajectory change.
At a given distancegravity has the greatest effect on trajectory for an arrow flying horizontallyand has gradually less effect as the shooting angle is raised or lowered. The reason for this is that the trajectory arc is determined by the horizontal distance the arrow travelsnot the overall distance. When shooting at steep angleseither up or downaiming for the actual distance to the target is a mistakesince this measurement may be considerably larger than the horizontal distance that governs the arrow's trajectory. For exampleif you shoot at a target 40 yards away down a steep hillusing your 40-yard sight pinyour shot will probably go high of the mark. At steep anglesyou must learn to compensate by aiming low.
Contrary to common opinionthis principle applies equally to uphill and downhill shots. It's true that uphill trajectory begins to differ from downhill trajectory at some pointbecause gravity slows an arrow flying up faster than one flying down. But within standard hunting distances-50 yards and less-the difference is not significant. For practical purposesthenslant range can be computed identicallywhether the slope is uphill or down.
The trickof courseis determining how low to aim at different distances and slope angles. You can calculate this information geometricallybut to do so requires a calculatorelectronic rangefinderclinometer for measuring the angle of slopes and a good head for mathematics.
If you choose the mathematical methodyou can simplify this work by using a chart like the example shown here. A complete chart for all practical shooting distances will help you make clean kills at steep angles. To put such a chart to practical usehoweveryou must know the distance to the target and angle of slope. Steep slopes make range estimation difficult at bestso a good rangefinder can help here. With practice you can learn to estimate slope visuallyor you can buy a compass with a built-in clinometer to measure slope. Oryou can buy an expensive forester's clinometerwhich measures angle of slope precisely.
To be honestusing mathematics to calculate shooting adjustments is not very practical for most hunters. In the fieldgame animals rarely give you enough time to make the measurements and computationsand few hunters are enthused by the prospect of carrying a rangefindercalculator and printed charts into the field.
Most shooters find that simple practice gives them a feel for how upward and downward angles affect arrow trajectory. You can practice by shooting from a tree stand set to different heightsfor example. At each heightshoot several groups at varying distances from your stand.
Reducing Trajectory
Flattening the trajectory of an arrow reduces the need for precise range estimationstreamlines the process for shooting over and under obstacles and simplifies adjustments needed when shooting at upward and downward angles. Several factors-fletching arrow weight and air density-can affect trajectorybut arrow speed has the single greatest influence. For this reasonmanufacturers and archers continually seek ways to make their bows faster and faster.
You can increase arrow speed in several ways. One method is to reduce arrow weight. Each 5-grain reduction in arrow weight provides a speed increase of about 1 foot per second (fps). Thusif you reduce arrow weight by 100 grainsyou increase speed by roughly 20 fps.
Arrow speed can also be gained by increasing the draw weight of the bow. A 1-pound increase in draw weight yields an increase of about 2 fps in speed. Thus if you crank draw weight up by 10 poundsyou gain 20 fps in arrow speed.
Finallyshooting a bow with harder cams can increase speed. At a given draw weighthard cams can provide 10 to 20 percent more speed than round wheels.
Up to a pointspeed is good. But remember that the faster the arrowthe more "critically" it shoots. That isfaster arrows are more susceptible to uncontrolled oscillations and are more difficult to shoot with accuracy. At some pointthe loss in accuracy and consistency that comes with ultrafast arrows may negate any gains you get from the flattened trajectory. Faster arrows also make it harder to tune the bowespecially when the arrows are equipped with broadheads.
Rememberaccuracy is the number-one ingredient in clean kills. Lightning-fast arrows do you no good if they don't consistently hit the target.
Using Geometry to Calculate Arrow Trajectory
Here's how geometry can be used to calculate how arrow trajectory changes when shooting on an incline:
Visualize the hunting situation as a right-angle trianglewith two perpendicular legs; (A)the distance from the hunter to the ground; and (B)the distance from the animal to the ground directly below the hunter. The sloped hypotenuse(C)is the distance from the hunter to the animal. In essencethe drop of an arrow fired along the inclined hypotenuse will equal the drop of an arrow traveling the horizontal distance (B).
For exampleimagine you're on a cliffwhere you spot a buck standing below at a 45-degree angle to your line of sight. Your rangefinder shows that the distance along the sloped line to the buck is 30 yards. Using a basic formula from geometrycalled the Pythagorean Theorem (A2 + B2 = C2)you can calculate that side Brepresenting the horizontal distance to the deeris roughly 21 yards. To hit the deer in the kill zonethenyou would use the 20-yard sight pinnot the 30-yard pin.
