What is mach number? And how does speed relate to mach numbers? That’s what we are going to talk about in this article!
A very popular way to determine vehicle top speeds is via the formula V = 0.62 * (mach)^2 * road surface area. The reason why most people use this equation is because it seems easy to understand, and you can calculate it quickly with just simple math.
But there are two major problems with using this equation to find top speeds. First of all, its accuracy is quite dependent on the accuracy of your measurements.
Second, even if you have accurate measurements, the formula assumes that the car is traveling at constant velocity. But cars are never completely still — especially race vehicles like dragsters!
So while this speed calculation method may work for average street drivers, it will not give you the exact same results when racing or doing donuts in the rain.
Fortunately, there is another much more reliable way to measure top vehicle speeds which has been time tested and proven. It was first proposed by German mathematician Daniel Bernoulli back in 1737!
Daniel Bernoulli’s Principle states that an object moving through air transfers some of its kinetic energy to the surrounding fluid. This happens as the object pushes away pieces of air from itself, creating an empty space behind it.
History of the mach number
The word “mach” comes from an Austrian scientist Fritz Reiner, who in 1908 calculated what he called the “relative velocity” or speed of an object based on how fast you could watch it move away. His most famous work was his calculation of the relative speed of earth vs. moon as 1 millimeter per day (or about 0.04 inches/hour).
He then integrated this time into the equation to determine the lunar landing speed for space vehicles! This is now known as the average orbital speed of the moon, which we can calculate by multiplying its mean diameter times π.
Since the moon’s average density is 3.9 tons per cubic mile, we can use that to find its average volume. Its surface area is 4π*(2 r)², where r is its radius. Taking these three equations together gives us the value of the absolute difference between the two speeds, or our new mach number!
His final result was 9.5, making the moon seem like it was going at full throttle compared to earth. In fact, it takes just over half a second longer for the moon to get out of earshot than it does for it to reach escape velocity!
This isn’t too surprising given that the moon has almost no atmosphere to slow down orbiting objects.
Compressibility effects
Even though we’ve discussed how drag increases as velocity rises, there is one more important factor to consider when talking about top speed of an object-compressibility.
As you increase your vehicle’s speed, air molecules are moving faster too, which means they need to pack in closer together. As these packed together atoms and molecules pull on the surface of the car being driven, it creates friction or resistance.
This resistance can be felt in two ways – energy loss due to heating up and reduced pressure caused by the thinning out of the fluid. The thinner the liquid, the greater the resistance to movement.
When thinking about compressibility, engineers take this into account by using formulas that calculate the effective density of the fluid based on its normal state and then subtracting off the average effective density at lower speeds. This effectively gives us the “effective density” of the fluid at higher speeds!
Using our example from before, if we were traveling at mach 5 with dry ice, then our water would freeze and turn into solid carbon dioxide gas, reducing our fluid volume and thus our overall drag force. Because dry ice is very dense (more so than any other fluid) however, its bulk density becomes even larger, making it even harder to escape the gravitational field.
By applying this concept to airplanes, pilots have found that the best way to gain speed is not going as fast as possible, but instead finding the optimal cruise altitude.
Special effects of temperature on mach number
As you can probably tell, as your mach number gets higher, things become more dangerous for you and the environment around you.
As your speed increases, so does the velocity of the air that is being pushed away from you. More rapidly moving air means colder air, which creates an uncomfortable feeling for people close to you and potentially bad weather conditions.
This effect goes beyond just making you feel cold, however. The faster you are going, the hotter the air becomes as it breaks down into smaller particles.
These hot, dense particles spread out as the air cools, creating darker, heavier clouds that make it harder to see where you are going.
Maximum mach number
The maximum speed you can achieve depends on two main things: your engine’s RPM, and how fast the air is moving around you. As we discussed before, faster speeds require higher revolutions per minute (RPM) of your engine, as well as faster airflow which produces more thrust.
The best way to determine how fast the air is traveling around you is by looking at some standard charts that tell you the average speed of an airstream in various environments! If it’s going much faster than what these charts say, then you have something either blocking or slowing down the flow – like a heavy coat layer, or a large object right in its path.
By knowing this, if you are ever able to reach a given speed, you will know whether you have maxed out because you ran into a limit of your vehicle or yourself! Keep in mind though that even when you think you hit your max speed, there could be another factor keeping you from reaching it, such as wind resistance.
Minimum mach number
The minimum mach number is defined as the speed of sound at one foot above the surface level of the air you are in. This can vary depending on the altitude, temperature, and pressure. At sea level, it is around 742 miles per hour!
At higher altitudes or lower temperatures, the sonic speed increases proportionally. For example, if we go up 1,000 feet in elevation and drop the temperature 5 degrees, the minimum mach number will increase by about 6%.
The average cruise speed for an airplane is typically around 250-300 mph, so to achieve a mach ten speed, you would have to go way faster than that!
A lot of pilots try to reach mach ten for various reasons. Some like the feeling of power while flying, others enjoy watching the wind blow through their hair, and some think it looks cool. All three are good reasons to strive for a mach ten flight!
Disclaimer: Only pursue this feat if you have trained enough and are sure of yourself. You should always be aware of your surroundings during a flight, even more so when going fast. Also, make sure you know what kind of aircraft you are piloting before trying anything beyond a takeoff and landing.
Effects of air density on mach number
As you can see, speed is inversely proportional to mass, but it’s not just the weight of the object that makes an impact, but also how much space there is around it.
If there’s less empty space, then there’s less air for the object to push through, which decreases its effective velocity. This is why cars are faster than planes- they have more surface area for drag forces to work with!
But what if we made our car even heavier? Then less effect would be seen due to the reduced drag force. An extremely heavy vehicle could still reach higher speeds, but it will take longer to get there.
This is similar to how very tall or wide objects require more time to pass a given marker (in this case, the front bumper). When traveling at high speeds, air moves quickly too, so a heavy vehicle will need more time to gain the same amount of speed.
Another way to look at it is that as your speed increases, the average distance between yourself and any other particles or obstacles also rises. Because of this, there is less chance of hitting something, and thus slower acceleration.
Compressible flow
In compressible fluid flows, such as water or air, you do not need to worry about viscosity. This is different than solid matter, like water going through glass. With liquid, you can easily see how it moves and varies in density, but with gas there are no visible components to influence its speed.
This does not mean that drag due to viscosity does not exist for gasses, however! When a fluid element is moving faster than its surroundings, shear forces are generated at the surface of the fluid element. These friction-like effects are what causes drag.
The heavier the fluid element, the greater these frictional forces will be! For this reason, fluids with higher densities tend to create more drag because they take longer to move away from where the momentum was applied.
With compressive flows, the fluid is being sped up instead of slowed down, so there is no need to consider drag caused by viscous properties. Because of this, we only focus on two types of drag for gaseous flows: pressure drag and shock drag.
Incompressible flow
Another important factor in determining how fast something can travel is whether or not fluid can escape the area where it collapses. If fluid cannot leave the region, then the density of the liquid will play a bigger role than if there were openings for it to go through.
This is because denser liquids require less time to be compressed down so they can move faster! This is why water is almost twice as fast at 100 miles per hour as champagne, which is much more dense.
In fact, when you are traveling at very high speeds, air becomes negligible and what matters most is just the speed of the vehicle itself and gravity.
At this stage, drag forces become dominant over gravitational force. Drag comes from two main sources: friction caused by solid objects that the car hits, and pressure losses due to the structure of the vehicle.
By having a strong frame and good aerodynamics, we have minimized drag so now only resistance coming form the inertia of the vehicle and gravity affect how quickly it moves.
