Mach number (Mach) - Unit Information & Conversion

Quick Answer

What is a Mach Number? A Mach number is the ratio of an object's speed to the speed of sound in the surrounding medium. It tells you how fast something is moving relative to the sound waves it creates.

Key Thresholds:

• Mach 1 = The speed of sound (Sonic)
• Mach < 1 = Slower than sound (Subsonic)
• Mach > 1 = Faster than sound (Supersonic)
• Mach > 5 = Hypersonic (extreme speeds)

At standard sea level conditions (15°C / 59°F):

• Mach 1 = 767 mph = 1,235 km/h = 343 m/s = 661 knots

Important: Because the speed of sound changes with temperature, the actual speed of "Mach 1" is slower at high altitudes where the air is colder.

Quick Comparison Table

Mach Numbers at Sea Level (15°C)

Mach Number	Speed (mph)	Speed (km/h)	Speed (m/s)	Regime	Example
Mach 0.5	383 mph	617 km/h	171 m/s	Subsonic	Small aircraft
Mach 0.85	652 mph	1,050 km/h	291 m/s	Transonic	Commercial airliner
Mach 1	767 mph	1,235 km/h	343 m/s	Sonic	Sound Barrier
Mach 1.5	1,151 mph	1,852 km/h	515 m/s	Supersonic	F-16 combat
Mach 2	1,534 mph	2,469 km/h	686 m/s	Supersonic	Concorde cruise
Mach 3	2,301 mph	3,704 km/h	1,029 m/s	Supersonic	SR-71 Blackbird
Mach 5	3,836 mph	6,174 km/h	1,715 m/s	Hypersonic	Hypersonic missile
Mach 10	7,672 mph	12,348 km/h	3,430 m/s	Hypersonic	X-43A scramjet
Mach 25	19,180 mph	30,870 km/h	8,575 m/s	Re-entry	Space Shuttle

Mach Numbers at Cruise Altitude (35,000 ft, -57°C)

Mach Number	Speed (mph)	Speed (km/h)	Speed (m/s)	Example
Mach 0.85	574 mph	924 km/h	257 m/s	Boeing 787 cruise
Mach 1	660 mph	1,062 km/h	295 m/s	Sound barrier (cold air)
Mach 2	1,320 mph	2,124 km/h	590 m/s	Supersonic cruise

Note: At altitude, colder air = slower sound speed = lower mph for same Mach number.

Definition and Standards

Mathematical Definition

The Mach number (symbol: M or Ma) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound.

Formula: $$ M = \frac{u}{c} $$

Where:

• M is the Mach number (dimensionless)
• u is the local flow velocity (speed of the object relative to the fluid)
• c is the speed of sound in the medium at local conditions

Why is it dimensionless? Because you are dividing speed by speed (m/s ÷ m/s), the units cancel out. Mach number is a pure ratio, like a percentage—it has no units.

Speed of Sound Calculation

The speed of sound in an ideal gas depends on temperature:

Formula: $$ c = \sqrt{\gamma \cdot R \cdot T} $$

Where:

• γ (gamma) = ratio of specific heats (1.4 for air)
• R = specific gas constant for air (287 J/(kg·K))
• T = absolute temperature in Kelvin

Simplified for air: $$ c_{m/s} = 20.05 \sqrt{T_K} $$

Example at 15°C (288.15 K): $$ c = 20.05 \sqrt{288.15} = 20.05 \times 16.975 = 340.3 \text{ m/s} \approx 343 \text{ m/s} $$

Key insight: Sound speed increases with temperature. Hot air = faster sound. Cold air (high altitude) = slower sound.

The Five Speed Regimes

Aerodynamic forces, drag, and control characteristics change drastically at different Mach numbers:

1. Subsonic (M < 0.8)

• Air flows smoothly around the object
• No shock waves
• Drag increases gradually with speed
• All cars, most helicopters, propeller aircraft
• Airflow remains attached to surfaces

2. Transonic (0.8 < M < 1.2)

• Mixed subsonic and supersonic airflow
• Shock waves form on wing surfaces before the aircraft reaches Mach 1
• "Transonic drag rise"—drag increases dramatically
• Buffeting and control difficulties
• Modern airliners cruise at Mach 0.85 (just below transonic problems)
• Requires swept wings and careful design

3. Supersonic (1.2 < M < 5.0)

• Entire airflow is faster than sound
• Shock waves form a "Mach cone" trailing the object
• Sonic boom heard on ground
• Higher drag than subsonic, but predictable
• Requires sharp nose, swept or delta wings
• Fighter jets, Concorde, SR-71 operate here

4. Hypersonic (M > 5.0)

• Extreme speeds where air friction creates intense heat
• Air molecules dissociate (break apart) from heat
• Plasma forms around vehicle
• Requires heat shields (ceramic tiles, ablative materials)
• Space Shuttle re-entry, ICBMs, scramjets

5. High-Hypersonic (M > 10)

• Chemistry of air changes completely
• Thermal protection dominates design
• Re-entry vehicles from orbit
• Currently experimental

History and Evolution

Ernst Mach: The Pioneer (1838-1916)

Ernst Mach was an Austrian physicist, philosopher, and experimental psychologist whose work laid the foundation for supersonic aerodynamics.

1887: Breakthrough Visualization

• Mach developed schlieren photography to visualize airflow
• First photographs of shock waves around supersonic bullets
• Proved that projectiles create pressure waves that behave differently above and below sound speed
• Published groundbreaking paper: "On the Photographing of Projectiles in Flight"

Mach's Insight: He recognized that the ratio of object speed to sound speed was the critical parameter determining aerodynamic behavior—not the absolute speed itself. A bullet at 2,000 mph at sea level behaves the same as one at 1,320 mph at 35,000 feet if both are at Mach 2.

Beyond Physics: Mach also contributed to philosophy (Mach's principle influenced Einstein) and psychology (Mach bands in visual perception).

Jakob Ackeret: Naming the Number (1929)

Jakob Ackeret (1898-1981), a Swiss aeronautical engineer, formalized the term "Mach number" in his 1929 paper on supersonic wind tunnels.

Why the honor? Ackeret wanted to recognize Mach's foundational work, even though Mach himself never used the term. The scientific community immediately adopted it.

World War II: The Transonic Crisis (1940s)

As fighter aircraft became more powerful, pilots encountered terrifying problems approaching Mach 1:

The "Sound Barrier" Myth:

• Controls would lock up or reverse
• Aircraft would shake violently (buffeting)
• Some planes broke apart in dives
• Many believed Mach 1 was an impenetrable physical barrier

The Real Problem: Transonic airflow created shock waves on wings, disrupting lift and control. Aircraft weren't designed for it.

Innovations Required:

• Swept wings (delayed shock wave formation)
• All-moving tail stabilizers (maintained control)
• Thinner wing profiles
• Rocket or jet propulsion (enough power to push through)

Chuck Yeager: Breaking the Barrier (1947)

October 14, 1947: The Historic Flight

Pilot: Captain Charles "Chuck" Yeager, US Air Force test pilot Aircraft: Bell X-1 (rocket-powered, orange, nicknamed "Glamorous Glennis") Location: Muroc Dry Lake (now Edwards Air Force Base), California

The Flight:

• X-1 carried to 25,000 feet under a B-29 bomber
• Dropped, Yeager fired rocket engines
• Climbed to 43,000 feet
• Reached Mach 1.06 (700 mph at that altitude)
• First controlled supersonic flight in history
• Sonic boom heard on ground

Yeager's Condition: He had two broken ribs from a horseback riding accident two days earlier. He flew anyway, using a broom handle to close the cockpit door.

Impact: Proved the "sound barrier" was not a barrier—just an engineering challenge. Launched the supersonic age.

The Supersonic Age (1950s-1970s)

1954: First supersonic fighter enters service (F-100 Super Sabre) 1964: SR-71 Blackbird first flight—Mach 3.3 capability 1969: Concorde first flight—Mach 2.04 cruise speed 1976: Concorde enters commercial service (London-New York in 3.5 hours)

The Dream and Reality:

• Everyone expected supersonic travel would become routine
• Reality: Sonic booms banned over land, fuel costs enormous
• Only Concorde and Soviet Tu-144 entered service
• Both retired (Concorde 2003, Tu-144 1978)

Modern Era (2000s-Present)

Hypersonic Research:

• 2004: NASA X-43A reaches Mach 9.6 (scramjet)
• 2010s: Hypersonic missiles development (Russia, China, US)
• 2020s: Commercial supersonic revival attempts (Boom Supersonic, others)

Why No Supersonic Airliners Today?

• Sonic boom restrictions over land
• High fuel consumption (3x subsonic aircraft)
• Smaller passenger capacity
• Maintenance complexity
• Environmental concerns

Real-World Examples and Applications

Commercial Aviation

Subsonic Airliners (Mach 0.80-0.85):

• Boeing 737, 787: Cruise Mach 0.78-0.84 (about 500-570 mph)
• Airbus A320, A380: Cruise Mach 0.82-0.85
• Why this speed? Optimal fuel efficiency. Faster = transonic drag = much higher fuel burn
• Typical cruise altitude: 35,000-43,000 feet where colder air reduces fuel consumption

Concorde (Retired 2003):

• Cruise speed: Mach 2.04 (1,354 mph)
• Cruise altitude: 60,000 feet (above weather and other traffic)
• London to New York: 3 hours 30 minutes (vs 7-8 hours subsonic)
• Ticket price: $12,000+ round trip
• Nose drooped for landing visibility
• Only supersonic passenger aircraft in sustained service

Military Aviation

Fighter Jets:

• F-16 Fighting Falcon: Max speed Mach 2.0+ (1,500 mph)
• F-22 Raptor: Can "supercruise" (supersonic without afterburner) at Mach 1.8
• F-35 Lightning II: Max speed Mach 1.6
• Su-27 Flanker (Russian): Max speed Mach 2.35
• MiG-25 Foxbat (Russian): Max speed Mach 3.2 (designed to intercept SR-71)

Why Supersonic?

• Intercept enemy aircraft quickly
• Evade missiles
• Strategic advantage

The Trade-off: Afterburners burn massive fuel. Supersonic flight duration measured in minutes, not hours.

Reconnaissance:

• SR-71 Blackbird: Sustained cruise Mach 3.3 (2,200+ mph)
• Operational altitude: 85,000+ feet
• Titanium skin heated to 600°F from air friction
• Fuel tanks leaked on ground (designed to seal when hot and expanded)
• Never shot down—outran over 4,000 missiles fired at it
• Retired 1998 (satellites and drones replaced it)

Space Exploration

Re-entry Speeds:

• Space Shuttle: Re-entered at Mach 25 (17,500 mph)
• Apollo Command Module: Re-entered at Mach 36 (25,000 mph) from Moon
• Meteors: Enter atmosphere at Mach 50-200+ (burning up from friction)

Heat Shield Required:

• Shuttle: Ceramic tiles, 2,300°F surface temperature
• Apollo: Ablative heat shield (sacrificial material burns away)
• Without heat shield: Vehicle would vaporize

SpaceX Starship:

• Re-entry speed: Mach 25
• Uses steel skin with active cooling and ceramic tiles

Ballistics

Bullets:

• Most rifle bullets: Mach 2-3 (2,000-3,000 fps)
• You hear the supersonic "crack" (mini sonic boom) before the gunshot "bang"
• Subsonic ammunition: Mach 0.9 (used with suppressors/"silencers" for stealth)

Artillery Shells:

• Howitzer shells: Mach 2-2.5
• Railguns (experimental): Mach 7+ (6,000+ mph)

Nature and Unusual Examples

Whip Crack:

• The "crack" of a bullwhip is a mini sonic boom
• The tip of the whip exceeds Mach 1 briefly
• First human-made supersonic motion (invented ~5000 BC)

Pistol Shrimp:

• Snaps claw creating cavitation bubble
• Bubble collapse creates shock wave at Mach 1+
• Stuns prey with sonic shock

Meteorites:

• Enter atmosphere at Mach 50-200
• Create massive sonic booms (sometimes heard 100+ miles away)
• Friction creates bright streak (most burn up completely)

Common Uses Across Industries

1. Aerospace Engineering

Aircraft Design:

• Aircraft are designed specifically for their Mach regime
• Subsonic (M < 0.8): Rounded nose, straight or slight sweep wings
• Transonic (M 0.8-1.2): Swept wings, supercritical airfoils
• Supersonic (M 1.2-5): Sharp nose, highly swept or delta wings
• Hypersonic (M > 5): Waverider designs, blunt bodies for heat management

Wind Tunnel Testing:

• Subsonic wind tunnels (M < 0.3)
• Transonic wind tunnels (M 0.8-1.2)—most difficult to build
• Supersonic wind tunnels (M 1.5-5)
• Hypersonic wind tunnels (M 5-25)—very expensive, short duration

Instrumentation:

• Machmeter: Cockpit instrument showing Mach number
• Critical for high-altitude flight (indicated airspeed becomes misleading)
• Combines pitot-static system with temperature measurement

2. Meteorology

Jet Streams:

• High-altitude winds at 30,000-40,000 feet
• Can reach 200+ knots (Mach 0.3-0.4 at altitude)
• Airliners use tailwinds to save fuel (30-60 minutes on transatlantic flights)

3. Military Operations

Missile Classifications:

• Subsonic cruise missiles: Mach 0.7-0.9 (Tomahawk)—stealthy, long range
• Supersonic missiles: Mach 2-3 (most anti-aircraft missiles)—fast interception
• Hypersonic missiles: Mach 5+ (under development)—extremely difficult to intercept

Sonic Boom Management:

• Military supersonic flight over land restricted
• Special clearance required
• Training ranges over unpopulated areas

4. Automotive (Land Speed Records)

ThrustSSC (1997):

• Only land vehicle to officially break sound barrier
• Mach 1.02 (763 mph) at Black Rock Desert, Nevada
• Driver: Andy Green (RAF pilot)
• Two Rolls-Royce jet engines from Phantom fighter
• Created sonic boom on land

Bloodhound LSR (in development):

• Target: Mach 1.3+ (1,000+ mph)
• Combination jet and rocket engines

Conversion Guide

Mach to mph (at Sea Level, 15°C)

Formula: $$ \text{mph} = M \times 767.269 $$

Quick Mental Math: Multiply by 770

Mach	mph (Exact)	mph (Mental Math)
0.5	384	385
0.85	652	655
1.0	767	770
1.5	1,151	1,155
2.0	1,534	1,540
3.0	2,302	2,310

Mach to km/h (at Sea Level, 15°C)

Formula: $$ \text{km/h} = M \times 1,234.8 $$

Quick Mental Math: Multiply by 1,235

Mach	km/h
0.5	617
1.0	1,235
2.0	2,470
3.0	3,704

Mach to m/s (at Sea Level, 15°C)

Formula: $$ \text{m/s} = M \times 343 $$

Mach	m/s
0.5	171.5
1.0	343
2.0	686
5.0	1,715

Temperature Effect on Mach Conversions

Speed of sound varies with temperature:

Condition	Temperature	Mach 1 (mph)	Mach 1 (m/s)
Sea level, standard	15°C (59°F)	767 mph	343 m/s
Hot desert	40°C (104°F)	799 mph	357 m/s
Cruise altitude	-57°C (-70°F)	660 mph	295 m/s
Arctic winter	-40°C (-40°F)	698 mph	312 m/s

Formula for Mach 1 speed: $$ c_{m/s} = 20.05 \sqrt{T_K} $$

Where T_K is temperature in Kelvin (K = °C + 273.15)

Common Conversion Mistakes

Mistake #1: Assuming Mach 1 is a Fixed Speed

Wrong: "Mach 1 is always 767 mph."

Right: "Mach 1 is 767 mph at sea level (15°C), but only 660 mph at cruise altitude (-57°C)."

Why it matters: An airliner doing 600 mph:

• At sea level (15°C): Mach 0.78—safe and subsonic
• At 35,000 feet (-57°C): Mach 0.91—dangerously close to sound barrier for subsonic aircraft

Real consequences: Exceeding the aircraft's Maximum Mach Number (MMO) can cause loss of control, structural damage, or buffeting.

Mistake #2: Confusing Ground Speed with Mach Number

Wrong: "If I have a 100 mph tailwind, my Mach number increases."

Right: "Mach number is based on airspeed (speed relative to air), not ground speed."

Example:

• Flying at Mach 0.85 (574 mph true airspeed at cruise altitude)
• 100 mph tailwind
• Ground speed: 674 mph
• Mach number: Still Mach 0.85 (air doesn't care about ground)

Why it matters: Aerodynamic forces (drag, lift, structural loads) depend on Mach number, not ground speed.

Mistake #3: Ignoring the Medium

Wrong: "Mach 1 in water is 767 mph."

Right: "Sound travels much faster in water (~3,300 mph), so Mach 1 in water is ~3,300 mph."

Examples:

• Air (15°C): 767 mph
• Water (25°C): ~3,300 mph
• Steel: ~13,000 mph
• Diamond: ~27,000 mph

Submarines: Never approach Mach 1. Fastest submarine: ~50 mph = Mach 0.015 in water.

Mistake #4: Comparing Mach Numbers at Different Altitudes

Wrong: "The F-22 cruises at Mach 1.8, so it's slower than the Concorde at Mach 2.04."

Context needed:

• F-22 at 50,000 feet: Mach 1.8 ≈ 1,190 mph
• Concorde at 60,000 feet: Mach 2.04 ≈ 1,350 mph

Both are supersonic, but actual speed difference is only 160 mph—Mach number alone doesn't tell the whole story without altitude context.