Projectile & Launch Studio
Where a shot lands, how fast it has to leave to get there, and the two launch angles that both hit the same target. One of them is almost always the better shot.
Inputs
The shot
Speed the object actually leaves at, which is not your flywheel surface speed. The flywheel studio works that out.
Floor to the point the object leaves the robot.
The target
The field is 144" across, so most shots are well under that.
How far above or below the target still scores. A goal mouth is bigger than a point.
Reality
Fire at a known distance, compare with the flat-ground range below, and put the ratio here. 100 means no losses, which is never true.
Results
Does this shot land?
—
Height when it gets there
—in
Misses the target by
—in
Range on flat ground
—in
Highest point
—in
Time in the air
—sec
Speed needed at this angle
—ft/s
Angle for maximum range
—°
The two angles that hit this target
At a fixed speed, a target that can be reached at all can be reached two ways: a flat fast shot and a lobbed one. They behave very differently.
Trajectory
Show the numbers behind this chart
Height of the shot at each point along its flight, the same values the curve above is drawn from.
How this is calculated
Once an object leaves the robot, nothing is pushing it. Horizontal speed stays put and vertical speed loses to gravity, which gives the familiar pair:
x(t) = v·cos(θ)·t y(t) = h + v·sin(θ)·t − ½·g·t²Eliminating time gives the height at any distance, which is the number that actually matters when you are aiming at something:
y(x) = h + x·tan(θ) − g·x² ÷ (2·v²·cos²(θ))With your numbers
Why two angles hit the same target
Rearranged for the angle, that equation is a quadratic in tan(θ), so it has two roots. Both send the object through the same point at the same speed:
- The flat shot. Gets there quickly, so a moving target or a moving robot has less time to ruin it. It arrives shallow, which matters if the goal wants the object dropping in.
- The lofted shot. Arrives steeply, drops into goals nicely, and clears things in the way. It hangs in the air far longer, which gives every error more time to compound.
The flat shot is usually the better competitive choice, because time of flight multiplies every aiming error. The lofted one is worth it when the goal geometry demands a steep arrival or something is in the way.
Forty-five degrees is not your best angle
The 45° rule holds only when you launch and land at the same height. Shooting from a robot at a raised goal, or from a raised launcher at the floor, moves the optimum. Launching from height h, maximum range comes at:
θ = atan( v ÷ √(v² + 2·g·h) )Which is always below 45°, and drops further the higher you launch from. It matters less than people expect near the optimum, though: the range curve is flat on top, so being a few degrees off costs very little. Being ten degrees off is a different matter.
What to trust here
The angles and the shape of the trajectory are reliable. The absolute ranges are not, until you have calibrated them against a real shot. That is the honest split: geometry and gravity are exact, and the air is not modeled at all.
Sources & assumptions
No VEX data is used beyond the 144" field width, quoted for scale. Everything else is projectile motion under constant gravity, which does not change between seasons.
Assumes a vacuum: no air resistance, no lift from spin, no wind. A backspinning object generates real lift and flies flatter and further than this predicts, which is one reason single-flywheel shooters are popular and another reason to calibrate against a real shot rather than trusting the number.
Treats the object as a point. Its size matters when the margin at the target is small, so the vertical margin is yours to set honestly.
Save this run, and compare
Keeps what is on screen so you can change something and see both sides of the change. Saved in this browser only, never uploaded.
Make a notebook page
Turns this calculation into a dated engineering notebook page: the setup, data, results, figures, working and sources, numbered and cited. You add the goal, the decision and the reflection in your own words, plus photos and sketches. Print it, paste it into Google Docs, or download a Word file or slides.
Where this goes next
Explore further on the full mapWhere the answers on this page can be used, and which tools could have given you the numbers it asks for.
Comes after
Flywheel Design Studiofills in your exit velocity hereCatapult & Puncher Energyfills in your exit velocity hereShooter Accuracy & Consistencygives you your position errorYou are here
Projectile & Launch Studio
Where your answer goes
Shooter Type Comparatorcompare which shooter type can reach the launch speed you needbrings your exit velocity with itFlywheel Design Studiopick a flywheel size and gearing that throws the object that fastCatapult & Puncher Energyfind how many bands and how much pull back give that launch speedShooter Accuracy & Consistencytest real shots to see how far they land from what the maths predictsuses your position error againa number carries across the next question it raises