Foot per second to Mach number Converter
Convert feet per second to Mach numbers with our free online speed converter.
Quick Answer
1 Foot per second = 0.000889 Mach numbers
Formula: Foot per second × conversion factor = Mach number
Use the calculator below for instant, accurate conversions.
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Foot per second to Mach number Calculator
How to Use the Foot per second to Mach number Calculator:
- Enter the value you want to convert in the 'From' field (Foot per second).
- The converted value in Mach number will appear automatically in the 'To' field.
- Use the dropdown menus to select different units within the Speed category.
- Click the swap button (⇌) to reverse the conversion direction.
How to Convert Foot per second to Mach number: Step-by-Step Guide
Converting Foot per second to Mach number involves multiplying the value by a specific conversion factor, as shown in the formula below.
Formula:
1 Foot per second = 0.00088863 Mach numbersExample Calculation:
Convert 60 feet per second: 60 × 0.00088863 = 0.0533178 Mach numbers
Disclaimer: For Reference Only
These conversion results are provided for informational purposes only. While we strive for accuracy, we make no guarantees regarding the precision of these results, especially for conversions involving extremely large or small numbers which may be subject to the inherent limitations of standard computer floating-point arithmetic.
Not for professional use. Results should be verified before use in any critical application. View our Terms of Service for more information.
Need to convert to other speed units?
View all Speed conversions →What is a Foot per second and a Mach number?
and Standards
The foot per second is defined as:
US Customary Definition
1 ft/s = the velocity of a body that travels a distance of one foot in a time interval of one second.
Formula: v (ft/s) = distance (feet) / time (seconds)
Exact SI conversion (since 1959 International Yard and Pound Agreement):
- 1 ft/s = 0.3048 m/s (exactly)
- 1 foot = 0.3048 meters (exactly)
Why ft/s Instead of mph?
Time scale appropriateness: Many technical applications involve sub-second events:
- Ballistics: Bullet flight time measured in milliseconds (0.001 seconds)
- Reaction distance: Driver reaction (1-2 seconds) × speed in ft/s = distance in feet
- Hydraulics: Flow velocities through pipes/channels measured continuously, not per hour
Intuitive scale for small objects:
- "Arrow travels 300 ft/s" vs "arrow travels 205 mph"—ft/s gives clearer sense of per-second distance
- Easier mental math: "How far does projectile travel in 0.1 seconds?" → 30 feet (at 300 ft/s)
Engineering calculations: US hydraulic formulas (Manning's, Darcy-Weisbach) use ft/s natively
Standard Conversions
Imperial/US conversions:
- 1 ft/s = 0.681818 mph (or 15/22 mph exactly)
- 1 ft/s = 3,600 feet/hour
- 1 ft/s = 720 feet/minute
Key conversion (memorize):
- 60 mph = 88 ft/s (exactly: 60 × 5,280 ÷ 3,600 = 88)
- 1 mph = 1.46667 ft/s (or 22/15 exactly)
Metric conversions:
- 1 ft/s = 0.3048 m/s (exactly)
- 1 ft/s = 1.09728 km/h
- 1 ft/s = 30.48 cm/s
Marine/aviation:
- 1 ft/s = 0.592484 knots
- 1 ft/s = 0.000888 Mach (at sea level, 68°F)
Relationship to Acceleration
Feet per second squared (ft/s²) measures acceleration:
- Gravity: g = 32.174 ft/s² (standard gravity, often rounded to 32.2 ft/s²)
- Car acceleration: 0-60 mph in 5 seconds = 88 ft/s ÷ 5 = 17.6 ft/s² average
- Comparison: SI gravity = 9.80665 m/s²
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
Note: The Foot per second is part of the imperial/US customary system, primarily used in the US, UK, and Canada for everyday measurements. The Mach number belongs to the imperial/US customary system.
History of the Foot per second and Mach number
and Evolution
Ancient Feet to Modern Standardization
The foot through history:
- Ancient civilizations: Egyptian, Greek, Roman feet varied (285-335 mm)
- Roman pes: ~296 mm (11.65 inches)—basis for many European feet
- Medieval England: Multiple feet existed regionally (London foot, York foot)
- 1588: Queen Elizabeth I attempted standardization
- 1824: British Imperial system defined foot as 1/3 yard
- 1959: International Yard and Pound Agreement defined 1 foot = 0.3048 meters exactly
The second:
- Originally: 1/86,400 of mean solar day (Earth's rotation)
- 1967: Redefined using cesium-133 atomic transition (9,192,631,770 cycles = 1 second)
- Modern definition independent of Earth's rotation (which varies slightly)
The Foot-Pound-Second (FPS) System
British engineering standard (1800s-1960s):
- Length: foot (ft)
- Mass: pound (lb)
- Time: second (s)
- Force: poundal (1 lb·ft/s²) or pound-force (lbf)
- Energy: foot-poundal or foot-pound-force (ft·lbf)
- Velocity: feet per second (ft/s)
FPS system applications:
- Railway engineering: Train speeds, braking distances
- Ballistics: Muzzle velocity, projectile range calculations
- Hydraulics: Water flow in pipes, channels, rivers
- Structural engineering: Wind loads, beam deflections
Decline and persistence:
- 1960: SI system established internationally
- 1970s-1980s: Most countries transitioned to metric
- US holdout: American industry, construction, and firearms sectors retained FPS
- Current: US ballistics universally uses ft/s; engineering mixed (metric in automotive/aerospace, imperial in civil/construction)
Ballistics and the ft/s Standard
Why ballistics uses ft/s:
- Historical momentum: 19th-century firearms development used FPS system
- Industry standardization: Millions of existing specifications in ft/s
- Practical scale: 1,000-3,000 ft/s range fits projectile velocities well
- Reloading data: Powder charge tables, pressure curves all in imperial units
Ammunition velocity standards (all in ft/s):
- .22 LR: 1,200-1,700 ft/s
- 9mm Luger: 1,100-1,300 ft/s
- .45 ACP: 800-900 ft/s
- .223 Remington / 5.56 NATO: 3,000-3,300 ft/s
- .308 Winchester / 7.62 NATO: 2,600-2,800 ft/s
- .50 BMG: 2,800-3,000 ft/s
Chronograph measurements: All ballistic chronographs (devices measuring projectile speed) display in ft/s in US market.
US Hydraulic Engineering
Manning's Equation (open channel flow): v = (1.49/n) × R^(2/3) × S^(1/2)
Where:
- v = velocity in ft/s
- n = Manning's roughness coefficient
- R = hydraulic radius in feet
- S = channel slope (dimensionless)
Note: The 1.49 coefficient is specific to ft/s (metric version uses 1.0 with m/s)
US civil engineering applications:
- Storm drainage design
- Sanitary sewer sizing
- Irrigation canal design
- River and stream analysis
- Flood control structures
Persistence reason: US infrastructure built over 150+ years using imperial units—retrofitting millions of engineering drawings impractical.
Driver Education and Safety
The "60 mph = 88 ft/s" Rule:
Used universally in US driver education to teach reaction distance:
Reaction time (typical): 1.5 seconds Distance traveled (at 60 mph): 1.5 × 88 = 132 feet before braking begins
Stopping distance breakdown (60 mph on dry pavement):
- Reaction distance: 132 feet (time to perceive, react, move foot to brake)
- Braking distance: ~180 feet (actual braking to stop)
- Total stopping distance: ~312 feet (longer than a football field!)
Why ft/s is better than mph for this:
- Intuitive: "I travel 88 feet every second at highway speed"
- Easy calculation: seconds × ft/s = feet
- Using mph requires: mph × 1.467 × seconds = feet (harder mental math)
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
Common Uses and Applications: feet per second vs Mach numbers
Explore the typical applications for both Foot per second (imperial/US) and Mach number (imperial/US) to understand their common contexts.
Common Uses for feet per second
Across Industries
Ballistics and Firearms
- Ammunition specifications: All US ammo rated in ft/s muzzle velocity
- Chronograph testing: Velocity measurement devices display ft/s
- Ballistic calculators: Trajectory prediction software requires ft/s input
- Reloading data: Powder charge tables show expected ft/s velocities
Archery and Hunting
- Bow performance: IBO (International Bowhunting Organization) speed ratings in ft/s
- Arrow selection: Spine charts factor in bow speed (ft/s)
- Kinetic energy calculations: KE = (arrow weight × velocity²) ÷ 450,240 (weight in grains, velocity in ft/s → energy in foot-pounds)
US Civil Engineering
- Open channel flow: Manning's equation uses ft/s for rivers, canals, drainage
- Storm water management: Inlet design, detention pond sizing
- Sanitary sewer design: Minimum 2 ft/s to prevent settling
- Flood analysis: Peak flow velocities in ft/s
Driver Education and Safety
- Reaction distance teaching: "At 60 mph, you travel 88 feet every second"
- Following distance: "3-second rule" = 3 × 88 = 264 feet at 60 mph
- Crash reconstruction: Skid mark analysis uses ft/s for velocity calculations
Sports Science
- Baseball/softball: Pitch speed tracking (radar guns display ft/s or mph)
- Golf: Launch monitors measure clubhead and ball speed in ft/s
- Track and field: Sprint speeds converted to ft/s for analysis
Aviation (Limited Use)
- Rate of climb/descent: Feet per minute (fpm), but convertible to ft/s
- Ground speed calculations: Sometimes expressed in ft/s for short-field operations
- Note: Aviation primarily uses knots (nautical miles per hour)
When to Use Mach numbers
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
Additional Unit Information
About Foot per second (ft/s)
Is ft/s faster than mph?
No—ft/s is a smaller unit, so the number is bigger for the same speed.
- 1 mph = 1.467 ft/s
- 100 ft/s = 68 mph (the ft/s number is bigger, but it's actually slower than "100 mph")
Think of it like inches vs feet: 12 inches = 1 foot. "12" is bigger than "1", but they're the same length. Similarly, "100 ft/s" looks bigger than "68 mph", but they're the same speed.
What is the speed of sound in ft/s?
Approximately 1,125 ft/s at sea level, 68°F (767 mph, 343 m/s) = Mach 1
Temperature dependence:
- 32°F (0°C): 1,087 ft/s
- 68°F (20°C): 1,125 ft/s (standard reference)
- 86°F (30°C): 1,145 ft/s
Practical rule: "Sound travels about 1,100 feet per second"
Lightning distance trick:
- See lightning flash
- Count seconds until thunder: "one Mississippi, two Mississippi, three..."
- Multiply seconds by 1,100 feet
- Divide by 5,280 (feet per mile) to get miles
- Example: 5 seconds → 5,500 feet → ~1 mile away
Why bullets are "supersonic" or "subsonic":
- Supersonic (> 1,125 ft/s): Creates sonic boom/crack
- Subsonic (< 1,125 ft/s): No sonic crack (quieter with suppressor)
How do I convert mph to ft/s in my head?
Method 1 (rough): Multiply by 1.5
- 60 mph × 1.5 = 90 ft/s (actual: 88, close!)
- 40 mph × 1.5 = 60 ft/s (actual: 58.7, pretty close)
Method 2 (better): Use the "22/15 rule" or remember key values
- 30 mph = 44 ft/s
- 60 mph = 88 ft/s
- 90 mph = 132 ft/s
- Scale from these: 45 mph = halfway between 30 and 60 → (44+88)/2 = 66 ft/s
Method 3 (precise): Multiply by 1.467 (or 22/15)
- 50 mph × 1.467 = 73.35 ft/s
Why do bullets use ft/s instead of mph?
Four main reasons:
- Historical: US firearms industry developed using FPS system (foot-pound-second)
- Practical scale: Bullet velocities (1,000-3,000 ft/s) fit well, whereas 700-2,000 mph sounds awkward
- Short-duration events: Bullets travel for fractions of a second, so "per second" is more intuitive than "per hour"
- Ballistic calculations: Easier math for drop (inches), time of flight (milliseconds), energy (foot-pounds) when velocity is in ft/s
Example: .223 Rem bullet at 3,200 ft/s
- Distance in 0.1 seconds: 320 feet (easy mental math)
- If stated as 2,182 mph: distance in 0.1 sec requires mph × 1.467 × 0.1 = 320 feet (harder)
What is terminal velocity in ft/s?
Human skydiver:
- Belly-to-earth (stable, arms/legs spread): 176 ft/s (120 mph, 54 m/s)
- Head-down streamline (diving position): 295 ft/s (200 mph, 90 m/s)
- With parachute deployed: 15-25 ft/s (10-17 mph)—safe landing speed
Other objects:
- Raindrop (small, 1mm): 20 ft/s
- Raindrop (large, 5mm): 30 ft/s
- Baseball: 146 ft/s (100 mph)
- Penny (myth-busting): 30-50 ft/s (not lethal!)
- Bowling ball: 335 ft/s (228 mph)—dangerous!
Why terminal velocity varies: Air resistance balances weight. Bigger, heavier, or more streamlined = higher terminal velocity.
How fast is 300 ft/s in mph?
300 ft/s = 204.5 mph
Formula: 300 ft/s × 0.682 = 204.5 mph
Context: This is a common archery speed (compound bow arrow) or paintball velocity limit (280-300 ft/s)
Comparison:
- 300 ft/s = subsonic (below 1,125 ft/s speed of sound)
- 300 ft/s = 91.4 m/s (metric)
- 300 ft/s = 199 knots (marine/aviation)
What does "subsonic ammo" mean?
Subsonic ammunition: Muzzle velocity < 1,125 ft/s (speed of sound)
Why use subsonic:
- No sonic crack: Supersonic bullets create a sonic boom as they break the sound barrier—sounds like a loud "crack"
- Suppressor-friendly: With a suppressor (silencer), subsonic ammo is much quieter—only the muzzle blast is heard, not the sonic crack
- Hearing protection: Even without suppressor, subsonic is less loud
Common subsonic rounds:
- .45 ACP: 850-900 ft/s (naturally subsonic, heavy bullet)
- 9mm subsonic: 950-1,050 ft/s (special loads, lighter powder charge)
- .22 LR subsonic: 1,050-1,100 ft/s
Supersonic ammunition: Velocity > 1,125 ft/s
- Standard .223 Rem: 3,200 ft/s (almost 3× speed of sound!)
- Standard 9mm: 1,200 ft/s (just barely supersonic)
How far does a car travel in 1 second at 60 mph?
88 feet (exactly)
Breakdown:
- 60 mph = 60 miles/hour
- 60 miles/hour × 5,280 feet/mile ÷ 3,600 seconds/hour = 88 feet/second
Why this matters for safety:
- Reaction time: Average driver takes 1.5 seconds to react to hazard
- Distance during reaction: 1.5 seconds × 88 ft/s = 132 feet (before even touching brake!)
- Braking distance: Additional ~180 feet to stop (dry pavement)
- Total stopping distance: 132 + 180 = 312 feet at 60 mph
Following distance "3-second rule":
- At 60 mph, maintain 3 × 88 = 264 feet behind car ahead
- Gives 2× reaction distance (safer margin)
Can I use ft/s in scientific equations?
Yes, but you must use imperial units consistently:
Kinetic energy (imperial): KE (foot-pounds) = ½ × mass (slugs) × velocity² (ft/s)²
- 1 slug = 32.174 pounds-mass
- Or: KE (ft·lbf) = weight (lbf) × velocity² (ft/s)² / (2 × 32.2)
Force (imperial): F (pound-force) = mass (slugs) × acceleration (ft/s²)
- Or: F (lbf) = (weight in lbf / 32.2) × acceleration (ft/s²)
For scientific work, SI units (m/s, kg, Newtons, Joules) are strongly preferred:
- No slugs vs pounds confusion
- International standards require SI
- Easier unit conversions (all decimal)
Bottom line: You can use ft/s in calculations, but it's more complex than metric. For ballistics and US engineering where ft/s is standard, imperial equations exist. For research/publication, convert to m/s.
What's the difference between ft/s and ft/s²?
ft/s (feet per second): Velocity—how fast you're moving ft/s² (feet per second squared): Acceleration—how quickly your velocity changes
Example (free fall):
- Gravity acceleration: g = 32.2 ft/s²
- After 0 seconds: velocity = 0 ft/s
- After 1 second: velocity = 32.2 ft/s (acceleration added 32.2 ft/s)
- After 2 seconds: velocity = 64.4 ft/s (acceleration added another 32.2 ft/s)
- After 3 seconds: velocity = 96.6 ft/s
Car example (0-60 mph in 5 seconds):
- Change in velocity: 60 mph = 88 ft/s
- Time: 5 seconds
- Average acceleration: 88 ft/s ÷ 5 seconds = 17.6 ft/s²
About Mach number (Mach)
What is a sonic boom?
When an object travels faster than sound (Mach 1+), it creates pressure waves faster than they can propagate away. These waves pile up, forming a shock wave—a cone of intense pressure that trails the object like the wake of a boat.
The "Boom":
- When this cone passes over you, you hear a sharp double "boom-boom"
- First boom: nose shock wave
- Second boom: tail shock wave
- Sounds like thunder or an explosion
- Can rattle windows, set off car alarms
Damage Potential:
- Low-altitude supersonic flight: Can break windows, damage structures
- High-altitude supersonic flight: Boom reaches ground weakened, sounds like distant thunder
- Concorde cruised at 60,000 feet to minimize ground impact
Continuous: The sonic boom is continuous along the entire flight path, not just when "breaking" the barrier. Everyone below the flight path hears a boom as the cone passes over them.
Why did the Concorde stop flying?
Economic and Regulatory Challenges:
1. Sonic Boom Restrictions:
- Banned from supersonic flight over most land masses
- Limited to oceanic routes (transatlantic primarily)
- Reduced potential markets dramatically
2. Fuel Consumption:
- Burned 3x more fuel than subsonic jets per passenger
- 17 tons per hour at Mach 2 cruise
- Rising fuel costs made operation increasingly expensive
3. Limited Capacity:
- Only 92-120 passengers (vs 400+ on Boeing 747)
- Small market for ultra-premium tickets
- Round-trip London-New York: $12,000+ (1990s-2000s)
4. Maintenance Costs:
- Complex systems required extensive maintenance
- Only two operators (British Airways, Air France)
- No economies of scale
5. Air France Flight 4590 Crash (2000):
- Metal debris on runway punctured tire
- Debris hit fuel tank, caused fire
- 113 killed
- Led to temporary grounding, increased insurance costs
- Public confidence damaged
Final Flight: October 24, 2003 (British Airways)
Modern Revival Attempts: Companies like Boom Supersonic developing new supersonic airliners with quieter "boom" and better fuel efficiency. Target: 2029-2030 service entry.
Can a car go Mach 1 on land?
Yes—but only one has officially done it.
ThrustSSC (1997):
- Speed: 763 mph (Mach 1.016) on October 15, 1997
- Location: Black Rock Desert, Nevada
- Driver: Andy Green (Royal Air Force fighter pilot)
- Power: Two Rolls-Royce Spey jet engines (from Phantom fighter jets)
- Thrust: 110,000 lb (50,000 kg)
- Weight: 10.5 tons
- First land vehicle to create sonic boom
Challenges:
- Extreme instability at transonic speeds
- Required perfect desert surface (dry lake bed)
- Aerodynamic design critical (shaped like a fighter jet)
- Braking from 760 mph without flipping
Bloodhound LSR (In Progress):
- Target: 1,000 mph (Mach 1.3)
- Hybrid jet + rocket propulsion
- Same driver (Andy Green)
- Testing ongoing in South Africa
What is "Critical Mach Number"?
Critical Mach Number (Mcrit) is the speed at which airflow over any part of the aircraft first reaches Mach 1—even if the aircraft itself is flying slower than Mach 1.
Why This Happens:
- Air accelerates as it flows over the curved upper surface of wings
- Example: Aircraft flying at Mach 0.80, but airflow over wing reaches Mach 1.0
Consequences of Exceeding Mcrit:
- Shock waves form on wing surface
- Airflow separation behind shock waves
- Loss of lift (buffeting, "Mach tuck")
- Increased drag (transonic drag rise)
- Control problems
Typical Values:
- Straight wing aircraft: Mcrit ≈ 0.75-0.85
- Swept wing aircraft: Mcrit ≈ 0.85-0.92
- Supersonic fighters: Mcrit > 0.95
Maximum Mach Number (MMO):
- Regulatory limit for aircraft (e.g., MMO = 0.90 for Boeing 737)
- Pilots must not exceed this speed
How do pilots calculate Mach number?
Instrumentation:
1. Machmeter (Cockpit Instrument):
- Combines pitot-static pressure measurements with temperature
- Directly displays Mach number
- Standard on all jet aircraft
2. Flight Management System (FMS):
- Computer calculates Mach number continuously
- Uses air data sensors (pitot tubes, static ports, temperature probes)
- Displays on primary flight display
Manual Calculation: $$ M = \frac{TAS}{LSS} $$
Where:
- TAS = True Airspeed (from airspeed indicator + altitude + temperature correction)
- LSS = Local Speed of Sound = 38.94 × √T (where T is temperature in Kelvin)
Example:
- Altitude: 35,000 feet
- Temperature: -57°C = 216 K
- TAS: 487 knots
- LSS: 38.94 × √216 = 38.94 × 14.7 = 573 knots
- Mach: 487 ÷ 573 = Mach 0.85
Is Mach 10 possible for aircraft?
Yes—but extremely challenging.
Achieved (Unmanned):
- NASA X-43A (2004): Mach 9.6 (7,000 mph) for 10 seconds
- Scramjet (supersonic combustion ramjet) technology
- Hydrogen fuel
- Launched from B-52 bomber + rocket booster
- Unmanned test vehicle
Challenges at Mach 10:
1. Extreme Heat:
- Air friction generates 3,000°F+ surface temperatures
- Requires exotic materials (carbon-carbon composites, ceramics)
- Active cooling systems needed
2. Engine Technology:
- Turbojets don't work above ~Mach 3 (air too fast for compressor)
- Ramjets work Mach 3-6 (no moving parts)
- Scramjets needed above Mach 6 (air stays supersonic through engine)
- Very low thrust-to-weight ratio
3. Control:
- Hypersonic flight extremely unstable
- Milliseconds to react
- Requires autonomous flight control systems
Current Applications:
- Hypersonic missiles: Russia (Kinzhal, Avangard), China (DF-ZF), US (under development)
- Space access: Potential for single-stage-to-orbit vehicles
- Research: NASA X-51 Waverider (Mach 5.1 sustained, 2013)
What is the fastest Mach number ever achieved?
By Manned Aircraft:
- SR-71 Blackbird: Mach 3.3 (2,193 mph) sustained cruise
- X-15 rocket plane: Mach 6.72 (4,520 mph) in 1967—still holds record
By Unmanned Aircraft:
- NASA X-43A: Mach 9.6 (7,000 mph) in 2004
By Spacecraft:
- Space Shuttle re-entry: Mach 25 (17,500 mph)
- Apollo 10 (1969): Mach 36 (24,791 mph)—fastest manned vehicle ever
- Parker Solar Probe: Mach 550+ (430,000 mph relative to Sun)—fastest human-made object
By Natural Objects:
- Meteors: Mach 50-200+ entering atmosphere
Why do some fighter jets have "supercruise"?
Supercruise is the ability to fly supersonic (Mach 1+) without using afterburners.
Traditional Supersonic Flight:
- Requires afterburner (raw fuel sprayed into exhaust, ignited)
- Increases thrust 40-70%
- Burns 3-5x more fuel
- Can only sustain for minutes
Supercruise Advantages:
- Fuel efficiency: Supersonic cruise without afterburner
- Extended supersonic duration: Hours instead of minutes
- Lower heat signature: Harder to detect with infrared missiles
- Greater range: Less refueling needed
Aircraft with Supercruise:
- F-22 Raptor: Mach 1.8 supercruise
- Eurofighter Typhoon: Mach 1.5 supercruise
- Dassault Rafale: Mach 1.4 supercruise
- Concorde: Mach 2.04 supercruise (civilian application)
How It's Achieved:
- Extremely efficient engines (high bypass turbofans with afterburner)
- Aerodynamic design minimizing supersonic drag
- High thrust-to-weight ratio
How loud is a sonic boom?
Loudness varies by altitude and aircraft size:
Concorde:
- At 60,000 feet cruise: 100-110 decibels on ground (sounds like distant thunder)
- At 40,000 feet: 120+ decibels (can break windows)
Fighter Jet:
- Low-altitude supersonic pass: 130-140 decibels (painfully loud, like artillery)
- High-altitude: 90-100 decibels (loud but not painful)
Comparison:
- Normal conversation: 60 dB
- Lawn mower: 90 dB
- Rock concert: 110 dB
- Jet engine (close): 140 dB
- Gunshot: 160 dB
Perceived Impact:
- Overpressure: 1-2 pounds per square foot (psf) typical for Concorde at cruise altitude
- 5+ psf: Can break windows
- 10+ psf: Structural damage to buildings
Why Banned Over Land:
- Continuous disturbance along entire flight path
- Affects thousands of people per flight
- Disrupts wildlife
- Property damage lawsuits
Can shock waves be photographed?
Yes—through schlieren photography.
Technique:
- Uses light refraction to visualize air density gradients
- Invented by August Toepler (1864), refined by Ernst Mach (1887)
- Shock waves create sharp density changes = visible patterns
Modern Applications:
- Wind tunnel testing: Visualizing airflow over models
- Ballistics research: Photographing bullets in flight
- NASA testing: X-59 "quiet supersonic" aircraft development
- Airshows: Ground-based cameras capturing fighter jets' shock waves
Iconic Images:
- Ernst Mach's 1888 bullet shock wave photographs
- NASA's T-38 shock wave interaction photos
- Schlieren video of sonic booms passing over landscape
Smartphone Era:
- High-speed smartphone cameras can sometimes capture shock wave patterns from fighter jets with proper lighting conditions
Conversion Table: Foot per second to Mach number
| Foot per second (ft/s) | Mach number (Mach) |
|---|---|
| 0.5 | 0 |
| 1 | 0.001 |
| 1.5 | 0.001 |
| 2 | 0.002 |
| 5 | 0.004 |
| 10 | 0.009 |
| 25 | 0.022 |
| 50 | 0.044 |
| 100 | 0.089 |
| 250 | 0.222 |
| 500 | 0.444 |
| 1,000 | 0.889 |
People Also Ask
How do I convert Foot per second to Mach number?
To convert Foot per second to Mach number, enter the value in Foot per second in the calculator above. The conversion will happen automatically. Use our free online converter for instant and accurate results. You can also visit our speed converter page to convert between other units in this category.
Learn more →What is the conversion factor from Foot per second to Mach number?
The conversion factor depends on the specific relationship between Foot per second and Mach number. You can find the exact conversion formula and factor on this page. Our calculator handles all calculations automatically. See the conversion table above for common values.
Can I convert Mach number back to Foot per second?
Yes! You can easily convert Mach number back to Foot per second by using the swap button (⇌) in the calculator above, or by visiting our Mach number to Foot per second converter page. You can also explore other speed conversions on our category page.
Learn more →What are common uses for Foot per second and Mach number?
Foot per second and Mach number are both standard units used in speed measurements. They are commonly used in various applications including engineering, construction, cooking, and scientific research. Browse our speed converter for more conversion options.
For more speed conversion questions, visit our FAQ page or explore our conversion guides.
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Last verified: December 3, 2025