HELIOS PROVING GROUNDS / ACE CHALLENGES

Needle’s Eye

Calculate the burns. Commit the shot. Fly the impossible-looking route.

PLANNING · CLOCK STOPPED

Objective Drift backwards, fire through the marked slot, evade torpedo I and laser-intercept torpedo II as your round disables the turret. Leave with a full hull and every mine intact.

t = 0.00 s

● Mine · 190 m hull trigger⊙ Dashed · 260 m blast◇ Your prediction— Observed path

Speed

Review observed time No flight committed

The turret is protected by a closed ring of mine trigger zones. Only the round fits through the marked slot. Planning takes no simulation time.

Known map coordinates · metres

Fixed map axes: +x right, +y up. Each mine has a 26 m physical radius, a 190 m hull-trigger radius and a 260 m blast radius. The turret fits inside a 75 m radius and lies outside every mine’s blast.

Mine	x (m)	y (m)

Flight conditions Planning support

Flight brief & constants

One cannon round; one laser shot. Acceleration magnitude ≤ 4 m/s². Relative launch speed ≤ 600 m/s. Laser range 2,000 m; charge 10 s. Aim locks when charging starts.

Turret range 2,382.10 m; first charge 10 s; next launch 30 s later. Torpedoes start at 100 m/s and accelerate at 4 m/s² in their launch direction. They do not home.

Turret center (2,300, 620) m. Firing slot at x = 1,800 m, between y = 596 and 684 m. Aim near its center. Exit by the flight deadline: x < 450 m, 700 < y < 1,000 m, vₓ < −20 m/s, |vᵧ| < 5 m/s. Impact and interception must be within 0.15 s.

The bow stays along +x; thrusters change either velocity component. There is no drag, gravity or recoil in this exercise. Mine and damage rules are simplified classroom models.

1 · Calculate the burns

For each axis: v_f = v_i + at and d = v_it + ½at². Position after a burn is initial coordinate + displacement d. A coast has a = 0.

The suggested durations below define eight legs. For a sweeping route, target these successive velocities (m/s): (60, 0) → coast → (30, 10) → (0, 16) → (−20, 30) → coast → (−40, 0) → coast. Solve the accelerations; you can also design your own route.

At vₓ = 0, keep vᵧ ≠ 0. Turning your velocity through a curve is different from coming to a full stop.

2 · Calculate weapon timing

Use your position and velocity at firing time. v_round = v_ship + u, where u is launch velocity relative to the ship. Choose uᵧ to cancel the ship’s sideways velocity. Then use dₓ / v_round,x for travel time to the turret hull at x = 2,240 m.

Laser charge start = intended interception time − 10 s. Predict the second torpedo’s coordinates with its known launch state and constant acceleration; lock those coordinates as the laser aim. The sensor worksheet below helps obtain its launch data without revealing its future path.

Cannon fire at t (s)Launch uₓ (m/s)Launch uᵧ (m/s)Laser charge at t (s)Laser aim x (m)Laser aim y (m)

Second torpedo · sensor worksheet

This is a rehearsal briefing for the suggested route. At the second launch the ship is at (1,100, 410) m, moving (−20, +30) m/s. A different route changes the turret’s aim.

Launch coordinates: (2,240.2324, 625.2757) m.
Initial velocity: (−99.61269, +8.79277) m/s.
Acceleration: (−3.98451, +0.35171) m/s².

Use elapsed time since launch, not total mission time. The laser is a ray fired from your ship’s actual position; mines block it.

3 · Record your prediction

Predict the ship’s coordinates and velocity when the cannon fires. Your estimate stays visible even if it is wrong.

Predicted x (m)Predicted y (m)Predicted vₓ (m/s)Predicted vᵧ (m/s)

Committing preserves this prediction. Revisions become separate flights.

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Arcade completion is practice evidence. Instructor review verifies written work.

Needle’s Eye

Flight review