Shock Math Calculator vs TOEIC Master Pro

Shock Math is a fast, accurate compressible-aerodynamics calculator for students, engineers, and anyone working in high-speed gas dynamics. Solve isentropic, shock, and duct-flow relations in seconds — from any input variable, for any gas. COMPRESSIBLE FLOW, SOLVED • Isentropic flow — pressure, temperature, density, and area ratios, Mach angle, and Prandtl–Meyer angle • Normal shock relations — downstream Mach, static and stagnation pressure, temperature, and density ratios • Oblique shock relations — weak and strong solutions, wave angle, deflection angle, and normal Mach components • Conical shock relations — Taylor–Maccoll solution for cone angle, surface Mach number, and surface property ratios • Fanno flow — adiabatic flow with friction in a constant-area duct • Rayleigh flow — frictionless flow with heat addition • Ideal gas law — p = ρRT and pV = nRT, with flexible units • Scratch Pad — a quick built-in calculator for the numbers in between SOLVE FROM ANY VARIABLE Don't just go forward from Mach number. Enter a pressure ratio, temperature ratio, area ratio, wave angle, or Prandtl–Meyer angle and Shock Math finds the Mach number for you — subsonic or supersonic branch, your choice. ANY GAS, ANY GAMMA Set the ratio of specific heats (γ) to model air, combustion products, monatomic gases, or anything in between. Every relation respects your γ. PROVEN-ACCURATE MATH Version 1.6 rebuilt and independently verified the calculation engine. Every relation is cross-checked against the classic NACA Report 1135 tables and against independent reference implementations across a wide range of Mach numbers and specific-heat ratios — hundreds of checks, zero discrepancies. Forward and inverse solutions round-trip exactly. BUILT FOR REAL WORK • Clean, focused calculators — no clutter • Light and dark mode • Show or hide the calculators you use • Built-in reference notes explaining each set of relations • Apple Watch scratch pad for quick calculations Whether you're checking homework in a gas dynamics course, sizing a supersonic nozzle, or sanity-checking a CFD result, Shock Math gives you trustworthy numbers fast. Feedback and feature requests are always welcome from the in-app form.

Sharpen your TOEIC skills with 50 full-length practice tests built exactly like the official exam. Monitor your progress, review detailed answers, and prepare to reach your dream score with confidence. Contact Us: For questions, suggestions, or bug reports, please contact us at izi.app.pro@gmail.com. Privacy Policy: https://sites.google.com/view/toeic-master-pro/privacy Terms of Use: https://sites.google.com/view/toeic-master-pro/terms