This thread refers to ram air induction provided by the forward motion of the vehicle, not "ram tuning" of intake and exhaust systems designed to maximize volumetric efficiency in a specific rpm band (or smooth out variations in air flow which is a good reason to keep your Helmholtz resonator).
Theory
The basic formula for calculating ram air pressure is given by:
P = v squared(d)/2g
where, P = pressure in lb./sq. ft.; v = velocity in fps; d = density of air in lb./cu. ft.; g = acceleration of gravity in ft./sec.
As 1 mph = 1.466 fps, at sea level and at a temperature of 59* F (15* C) the normal density of dry air is .0765 lb./cu. ft. (1.225 kg/cu. meter) and g = 32.16 ft./sec., the formula for dynamic pressure is:
P = 1.466 squared(.0765)/64.32
P = .163765687/64.32 = .002546108 lb./sq. ft.
Therefore,
PSI = .002546108/144 = .000017681
Consequently, the dynamic pressure due to ram at any given vehicle velocity is given by the formula:
PSI = V squared(.00017681)
or,
PSI = V squared/56,550
where, PSI = ram air pressure in pounds/square inch; V = forward velocity of the vehicle in mph
The air density value used in the above formula applies only at sea level elevation, 59* F (15* C) temperature, and 0% relative humidity, standards defined by the International Standard Atmosphere (ISA) table. If temperature decreases below the standard, ram will increase due to the increased density of the air; if elevation or temperature increases above the standard, ram will decrease with the lowered air density.
Reference: High Speed Combustion Engines, 16th Edition, by P. M. Heldt; Chapter 24: Power Output and Other Characteristics, page 657.
As SAE Standard J1349 has supplanted the ISA as the protocol for determining BHP and torque in automobiles, the above formula can be configured to reflect those parameters. Since the latest standard is based on a higher temperature rating of 77* F (25* C), the normal density of dry air at sea level reduces to .0722 lb./cu. ft. (1.1568 kg/cu. meter). Thus the reconfigured formula for determining dynamic pressure due to ram at any given velocity becomes:
PSI = V squared/59,690
Here are some representative examples of the ram obtainable in PSI, inches of water, inches of mercury, and kilopascals at various vehicle velocities based on the ISA parameters. These measures have been selected because, as will be seen later, they're in common usage when developing actual ram air systems:
MPH______PSI____"Water_____"HG____kilopascal
55 ________ .053 ______ 1.5 _______ .11 ______ .372
60 ________ .064 ______ 1.77 ______ .13 ______ .441
65 ________ .075 ______ 2.07 ______ .15 ______ .515
70 ________ .087 ______ 2.41 ______ .18 ______ .600
80 ________ .113 ______ 3.13 ______ .23 ______ .779
90 ________ .143 ______ 3.96 ______ .29 ______ .986
100 _______ .177 ______ 4.90 ______ .36 ______ 1.220
110 _______ .214 ______ 5.92 ______ .44 ______ 1.475
120 _______ .255 ______ 7.06 ______ .52 ______ 1.758
130 _______ .299 ______ 8.28 ______ .61 ______ 2.062
Just for the fun of it:
168 _______ .500 _____ 13.84 _____ 1.02 ______ 3.447
238 ______ 1.00 ______ 27.68 _____ 2.04 ______ 6.895
In order to obtain these dynamic pressures, the air inlet must be placed in a high pressure area on the car and a reasonably efficient entry must be provided, for example, the use of a scoop or bell mouth. To make use of the ram air, the dynamic pressure of the air must be converted to static pressure by flowing it through a diffuser. In a road car, the air box can act as a diffuser of sorts slowing down the air velocity and consequently increasing its pressure. In a Formula 1 car, the forward-facing air intake is located above the driver's head. A diverging duct that acts as a diffuser leads the intake air from the inlet to the air box placed over the throttle bodies, in the process converting dynamic to static pressure.
One interesting point is that in many cases, the mean air velocity through any given part of the induction system caused by the downward movement of the pistons on the intake stroke is slower than the intake air velocity produced by the forward motion of the vehicle. To determine the former value, it's necessary to find the mean piston speed in ft./sec. at a given rpm and then use that to find the mean air velocity through the intake system at the same rpm. The result can then be compared with the velocity of the intake air due to ram. For example, let's make this comparison with the SkyActiv engine at a speed of 65 mph in 6th gear. Since the OEM analog tach is not accurate enough for this purpose, I calculated the rpm and obtained a value of 2,314. Since the stroke of the engine is 91.2 mm, we can now determine the piston speed in ft./sec. by using the formula:
Piston speed in ft./sec = rpm x stroke in mm/9144
therefore,
Piston speed = 2,314 x 91.2/9144 = 23.08 ft./sec.
Next, I selected the front of the fresh air duct no. 2 (Mazda's terminology) where it connects to no. 1 fresh air duct at the bulkhead at the front of the engine compartment as the point at which to calculate the air flow in the intake duct. Not wishing to take anything apart at this point (the car's only a couple of weeks old), I measured its O.D. with a caliper which was ~ 2 5/64" (2.078"; 52.5 mm) so I approximated its I.D. as 2" (50 mm) which is close enough for our purposes here. I also noted that, from it's connection to the no. 1 air duct which serves as the inlet, it gradually diverges in diameter as it connects to the no. 3 fresh air duct which also diverges in diameter until it connects to the air box. It looks to me that Mazda had ram air induction in mind when they designed this layout. Can this be possible?
Since the diameter of the bore of the SkyActiv engine is 83.5 mm, the next step is to calculate the mean air velocity due to the downward piston movement through the 2" I.D. section of the fresh air duct by multiplying the ratio of the diameter of the cylinder bore (D) to the diameter of the fresh air duct (d) by the already obtained piston speed in ft./sec, by using the formula:
Mean air velocity through intake duct = piston speed in ft. per sec. x (D/d)
Mean air velocity through intake duct = 23.08 x (83.5/50) = 38.54 ft./sec
References:
The Design and Tuning of Competition Engines, 5th Edition, by Philip H. Smith; Chapter 27: Definitions, Constants and Formulae, pages 457-460.
Auto Math Handbook, by John Lawlor; Chapter 3: Piston speed, pages 17-21
The final step is to calculate the air velocity in ft./sec. due to the forward motion of the vehicle. Since we already know that 1 mph = 1.466 ft./sec., then at 65 mph the intake air velocity due to ram = 95 ft./sec. thus, the ram air at this speed has a considerably higher velocity than does the air actually drawn into the cylinders. Ram air advocates assert that this may cause a pressure buildup behind the closed intake valves such that when they open there will be a slight pressure increase that will promote cylinder filling over what would have been the case without ram. This effect is not just an artifact of the low rpm operation in 6th gear at 65 mph. In 5th gear, the mean air speed = 47 ft./sec.; in 4th gear, 57 ft./sec.; and in 3rd gear, 77 ft./sec, all values still well below the air flow due to ram.
In my next post, we'll discuss methods of measuring air pressures throughout the intake system in order to quantify any positive results and look at some modifications to road cars that have yielded some surprisingly beneficial results due to enhanced ram effects. Perhaps we can even come up with some ways to improve air flow in the Sky?
Theory
The basic formula for calculating ram air pressure is given by:
P = v squared(d)/2g
where, P = pressure in lb./sq. ft.; v = velocity in fps; d = density of air in lb./cu. ft.; g = acceleration of gravity in ft./sec.
As 1 mph = 1.466 fps, at sea level and at a temperature of 59* F (15* C) the normal density of dry air is .0765 lb./cu. ft. (1.225 kg/cu. meter) and g = 32.16 ft./sec., the formula for dynamic pressure is:
P = 1.466 squared(.0765)/64.32
P = .163765687/64.32 = .002546108 lb./sq. ft.
Therefore,
PSI = .002546108/144 = .000017681
Consequently, the dynamic pressure due to ram at any given vehicle velocity is given by the formula:
PSI = V squared(.00017681)
or,
PSI = V squared/56,550
where, PSI = ram air pressure in pounds/square inch; V = forward velocity of the vehicle in mph
The air density value used in the above formula applies only at sea level elevation, 59* F (15* C) temperature, and 0% relative humidity, standards defined by the International Standard Atmosphere (ISA) table. If temperature decreases below the standard, ram will increase due to the increased density of the air; if elevation or temperature increases above the standard, ram will decrease with the lowered air density.
Reference: High Speed Combustion Engines, 16th Edition, by P. M. Heldt; Chapter 24: Power Output and Other Characteristics, page 657.
As SAE Standard J1349 has supplanted the ISA as the protocol for determining BHP and torque in automobiles, the above formula can be configured to reflect those parameters. Since the latest standard is based on a higher temperature rating of 77* F (25* C), the normal density of dry air at sea level reduces to .0722 lb./cu. ft. (1.1568 kg/cu. meter). Thus the reconfigured formula for determining dynamic pressure due to ram at any given velocity becomes:
PSI = V squared/59,690
Here are some representative examples of the ram obtainable in PSI, inches of water, inches of mercury, and kilopascals at various vehicle velocities based on the ISA parameters. These measures have been selected because, as will be seen later, they're in common usage when developing actual ram air systems:
MPH______PSI____"Water_____"HG____kilopascal
55 ________ .053 ______ 1.5 _______ .11 ______ .372
60 ________ .064 ______ 1.77 ______ .13 ______ .441
65 ________ .075 ______ 2.07 ______ .15 ______ .515
70 ________ .087 ______ 2.41 ______ .18 ______ .600
80 ________ .113 ______ 3.13 ______ .23 ______ .779
90 ________ .143 ______ 3.96 ______ .29 ______ .986
100 _______ .177 ______ 4.90 ______ .36 ______ 1.220
110 _______ .214 ______ 5.92 ______ .44 ______ 1.475
120 _______ .255 ______ 7.06 ______ .52 ______ 1.758
130 _______ .299 ______ 8.28 ______ .61 ______ 2.062
Just for the fun of it:
168 _______ .500 _____ 13.84 _____ 1.02 ______ 3.447
238 ______ 1.00 ______ 27.68 _____ 2.04 ______ 6.895
In order to obtain these dynamic pressures, the air inlet must be placed in a high pressure area on the car and a reasonably efficient entry must be provided, for example, the use of a scoop or bell mouth. To make use of the ram air, the dynamic pressure of the air must be converted to static pressure by flowing it through a diffuser. In a road car, the air box can act as a diffuser of sorts slowing down the air velocity and consequently increasing its pressure. In a Formula 1 car, the forward-facing air intake is located above the driver's head. A diverging duct that acts as a diffuser leads the intake air from the inlet to the air box placed over the throttle bodies, in the process converting dynamic to static pressure.
One interesting point is that in many cases, the mean air velocity through any given part of the induction system caused by the downward movement of the pistons on the intake stroke is slower than the intake air velocity produced by the forward motion of the vehicle. To determine the former value, it's necessary to find the mean piston speed in ft./sec. at a given rpm and then use that to find the mean air velocity through the intake system at the same rpm. The result can then be compared with the velocity of the intake air due to ram. For example, let's make this comparison with the SkyActiv engine at a speed of 65 mph in 6th gear. Since the OEM analog tach is not accurate enough for this purpose, I calculated the rpm and obtained a value of 2,314. Since the stroke of the engine is 91.2 mm, we can now determine the piston speed in ft./sec. by using the formula:
Piston speed in ft./sec = rpm x stroke in mm/9144
therefore,
Piston speed = 2,314 x 91.2/9144 = 23.08 ft./sec.
Next, I selected the front of the fresh air duct no. 2 (Mazda's terminology) where it connects to no. 1 fresh air duct at the bulkhead at the front of the engine compartment as the point at which to calculate the air flow in the intake duct. Not wishing to take anything apart at this point (the car's only a couple of weeks old), I measured its O.D. with a caliper which was ~ 2 5/64" (2.078"; 52.5 mm) so I approximated its I.D. as 2" (50 mm) which is close enough for our purposes here. I also noted that, from it's connection to the no. 1 air duct which serves as the inlet, it gradually diverges in diameter as it connects to the no. 3 fresh air duct which also diverges in diameter until it connects to the air box. It looks to me that Mazda had ram air induction in mind when they designed this layout. Can this be possible?
Since the diameter of the bore of the SkyActiv engine is 83.5 mm, the next step is to calculate the mean air velocity due to the downward piston movement through the 2" I.D. section of the fresh air duct by multiplying the ratio of the diameter of the cylinder bore (D) to the diameter of the fresh air duct (d) by the already obtained piston speed in ft./sec, by using the formula:
Mean air velocity through intake duct = piston speed in ft. per sec. x (D/d)
Mean air velocity through intake duct = 23.08 x (83.5/50) = 38.54 ft./sec
References:
The Design and Tuning of Competition Engines, 5th Edition, by Philip H. Smith; Chapter 27: Definitions, Constants and Formulae, pages 457-460.
Auto Math Handbook, by John Lawlor; Chapter 3: Piston speed, pages 17-21
The final step is to calculate the air velocity in ft./sec. due to the forward motion of the vehicle. Since we already know that 1 mph = 1.466 ft./sec., then at 65 mph the intake air velocity due to ram = 95 ft./sec. thus, the ram air at this speed has a considerably higher velocity than does the air actually drawn into the cylinders. Ram air advocates assert that this may cause a pressure buildup behind the closed intake valves such that when they open there will be a slight pressure increase that will promote cylinder filling over what would have been the case without ram. This effect is not just an artifact of the low rpm operation in 6th gear at 65 mph. In 5th gear, the mean air speed = 47 ft./sec.; in 4th gear, 57 ft./sec.; and in 3rd gear, 77 ft./sec, all values still well below the air flow due to ram.
In my next post, we'll discuss methods of measuring air pressures throughout the intake system in order to quantify any positive results and look at some modifications to road cars that have yielded some surprisingly beneficial results due to enhanced ram effects. Perhaps we can even come up with some ways to improve air flow in the Sky?