Case Study: Adding Real, Authentic Physics to a Tabletop Game
Project: PROJECTILE WAR (v2.0 Final)
Designer / Implementer: Guillermo Ithier (Physics Teacher & Game Designer)
Context: 11th Grade Physics — Ridgefield Park Junior/Senior High School
Focus: Translating real-world ballistics into playable tabletop damage using a GURPS-inspired √(Energy) conversion pipeline.
1) The Problem
Most “physics games” either:
- use physics as flavor text (numbers that don’t behave like the real world), or
- become a calculator exercise (accurate, but not fun).
My goal was to do the hard thing: make authentic physics drive the tactics while keeping turns fast enough for a 10–12 minute duel and smooth enough for a classroom block.
The specific challenge: How do you turn projectile behavior (mass, caliber, velocity) into damage that feels believable and plays well?
2) The Design Goal
Build a physics-forward combat model that is:
- Authentic: rewards real physical intuition (heavier, faster, denser projectiles hit harder).
- Readable: players can estimate outcomes without pausing the game.
- Balanced: produces a usable range of damage values for shields/cannons without runaway scaling.
- Teachable: reinforces core physics concepts naturally (density, velocity, energy scaling).
3) The Solution: A GURPS-Style Ballistics Conversion Pipeline
I implemented a ballistic conversion method inspired by GURPS’ √(Energy) approach, adapted into a tabletop-friendly procedure.
Core Concepts Implemented
- A) Bore / Caliber as the anchor
- Bore = internal barrel diameter (in inches).
- Caliber isn’t a “label”—it’s a physical measurement used in every calculation.
- B) Sectional Density (SD) as the penetration/impact proxy
SD captures a key real-world truth: a projectile’s weight relative to its diameter matters.
Two practical SD computation modes were used (depending on how projectile mass was presented):
- Weight in pounds (lb) or
- Weight in grains (gr)
The point wasn’t just correctness—it was flexibility, because real projectile data comes in both units.
- C) Velocity as the energy amplifier
Velocity is the big lever. Players don’t need to memorize kinetic energy equations to feel the truth:
speed dominates outcomes.
- D) √(Energy) into GURPS-style damage dice
The conversion step uses a square-root relationship so damage growth stays playable.
That’s the key design advantage: realistic scaling without breaking the game.
4) The Working Method (Tabletop-Ready Procedure)
This is the actual pipeline players (and my students) could follow consistently:
- Identity: Get C (true bore in inches).
- Density: Compute SD from projectile weight and caliber.
- Lookup: Find a P constant based on caliber (C) from a reference table.
- Convert: Use V (ft/s), SD, C, and P to compute D_raw.
- Round + Scale:
- round fractional dice sensibly
- apply the >12d scaling rule to keep results playable
This produced a system that was:
- accurate enough to “feel real,”
- consistent enough for design tuning,
- fast enough for classroom play.
5) How It Integrated Into PROJECTILE WAR
PROJECTILE WAR already had a clean tactical structure (Fire / Maintenance / Utility) and a physics-forward legality check (M × A ≥ F). The ballistics conversion system became the backend that made offensive cards physically honest.
Implementation Approach
Each Offensive card was treated like a “shell spec.”
Behind the scenes (during design/tuning), I used:
- Projectile weight → SD
- Caliber/bore → SD + lookup constant
- Muzzle velocity → energy driver
- √(Energy) conversion → damage dice band
Then I mapped results into the game’s needs:
- shield HP pacing
- stress risk (σ escalation)
- how quickly shields drop vs cannons being endangered
- preventing one “best shell” from dominating the deck
Result: the numbers didn’t just look scientific—they behaved scientifically in aggregate.
6) Examples That Proved the Model Was “Real Enough”
I used SD worked examples as sanity checks and as classroom-friendly anchors:
| Example | Weight | Caliber | SD (Result) |
| 1 | 6.1 lb | 3.67″ | 0.453 |
| 2 | 660 gr | 0.51″ | 0.362 |
| 3 | 10 lb | 2.00″ | 2.500 |
| 4 | 500 gr | 0.308″ | 0.753 |
| 5 | 1 lb | 1.00″ | 1.000 |
And quick practice exercises reinforced the “density intuition”:
- 300 gr, 0.30 in → SD ≈ 0.476
- 8 lb, 4.0 in → SD = 0.5
- 900 gr, 0.45 in → SD ≈ 0.635
Even without doing the full damage conversion mid-game, students could predict which shells should hit harder—because the SD math matched reality.
7) Classroom Implementation
Because I’m a physics teacher, I treated implementation as both system design and instructional design.
Classroom Goal
Students shouldn’t feel like they’re “doing a physics worksheet.”
They should feel like they’re making better tactical decisions, and the physics should quietly power that improvement.
What Students Learned Through Play
- Caliber and bore are physical measurements, not labels.
- Sectional density explains why “bigger” isn’t automatically “better.”
- Velocity is the damage amplifier.
- Square-root scaling is a real modeling tool: it keeps systems stable while remaining realistic.
8) What Worked (And Why)
1) Authenticity without slowdown
The conversion pipeline was used primarily for design tuning and reference truth. Gameplay stayed fast.
2) Predictable realism creates strategy
Because outcomes had a physical logic, students formed heuristics:
- “dense + fast is scary”
- “big bore isn’t automatically best”
- “rotation and maintenance matter because systems degrade”
3) It strengthened the core game tension
Realistic damage bands made the central choice sharper:
- fire aggressively → build stress (σ) → risk detonation
- stabilize → lose tempo
With physically grounded damage, those choices felt earned, not arbitrary.
9) What I Changed After Testing
Two implementation lessons echoed across both game design and classroom usability:
- Decision timing must be forced.
Players delayed Maintenance mode decisions → I required choosing mode on play. - Fast games need checklists.
Players missed σ/Φ updates during high tempo → I added an explicit end-turn checklist.
These weren’t physics problems—they were human factors problems. Fixing them made the physics system usable.
10) Outcomes
This implementation produced a rare combination:
- A competitive duel game that plays in 10–12 minutes
- Physics authenticity grounded in real ballistic principles (caliber, SD, velocity, √(Energy) scaling)
- A classroom-tested system that held up across repeated matches in one 85-minute block
11) Why This Matters (Portfolio Takeaway)
This project demonstrates that I can:
- translate real-world models into playable systems,
- preserve fun and pace under classroom constraints,
- and use iterative playtesting to solve the actual friction points.
PROJECTILE WAR isn’t “physics-themed.”
It’s a game where physics is the hidden engine that makes the tactics honest.
Appendix: Visual Reference Assets Used
- Cartridge cross-section diagram (Wikimedia / Wikipedia)
- Cartridge illustration still (YouTube source image)