Induction Math for High-Performance Engines

In Chapter 5, I discussed mean effective cylinder pressure and ways to measure or calculate it. When we consider the importance of the relationship between MEP and engine performance, we have to acknowledge where that pressure came from. It comes from the combustion (reaction) of the air and fuel mixture pushed into the cylinder on the intake stroke. The compression stroke squeezes the daylights out of it to increase its density and the spark plug lights it off to create combustion pressure (MEP) during the power stroke. Among other things, the pre-combustion density of the air/fuel charge in the cylinder determines MEP. The energy volatility of that combustion pressure is governed by mixture quality, chamber turbulence, spark timing, and a host of other contributors, but charge density is the compelling factor.

 


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Pro Stock and Pro Mod drag racing engines achieve VE percentages as high as 125 percent due to their narrow power band and the exceptional high speed efficiency of tunnel ram intake manifolds and split-Dominator style carburetors designed to take advantage of induction system wave tuning. (Courtesy Don Cooper/Reher & Morrison)


 

Engine Air Capacity

We can’t make a cylinder hold more than its physical dimensions, but we can increase the density of the gas captured within it. Hence the terms air capacity, volumetric efficiency, and inertial ram tuning. The earth’s atmosphere does us the courtesy of providing 14.7 psi of pressure to fill the cylinders for free. In a perfect world, the engine would inhale the exact swept volume of all its cylinders every two revolutions of the crankshaft. That represents its theoretical or potential air capacity. The following formula is used to calculate it.

Air Capacitycfm = (displacement x RPM) ÷ (1,728 x 2)

Note that air capacity is a function of displacement (volumetric capacity) and engine speed (RPM). The displacement is divided by 1,728 (the number of cubic inches in a cubic foot) to convert it to cubic feet. The RPM is divided by 2 because the engine only intakes on every other revolution. The formula can be simplified as follows:

Air Capacitycfm = (displacement x RPM) ÷ 3,456

In practice this formula is often useful to calculate the engine air requirement at both peak torque and peak power. Why? Because we want to know the minimum requirement at peak torque or the point of highest efficiency. Then we want to establish the maximum requirement at peak power so we can determine the effective airflow range of the engine under wide open throttle (WOT) conditions.

Let’s calculate the airflow requirement for a 350-ci engine with a torque peak at 5,300 rpm and a maximum engine speed of 6,500 rpm. First the torque peak:

CFM = (350 x 5,300) ÷ 3,456 = 536 cfm at the torque peak
And then the power peak:

CFM = (350 x 6,500) ÷ 3,456 = 658 cfm at the power peak These are the engine’s theoretical air requirements if we didn’t have all sorts of interference and restriction from carburetor venturis and throttle plates, manifold runners, intake ports, valves, and so on.

 

Volumetric Efficiency

In the preceding example the theoretical airflow capacity requires at least 536 cfm at the torque peak and 658 cfm at the maximum engine speed. These would be airflow requirements at WOT. So we need a 650-cfm carburetor, right? Not so fast. Many factors combine to reduce or in some cases increase the actual airflow requirement.

 

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Compare the 2-inch throttle bores on this 1,050-cfm Holley Dominator to the 19⁄16 throttle bores on the adjacent 600-cfm Holley street carburetor. Properly matching carburetor size to actual engine airflow requirements is critical to achieving optimum performance on the street or the track. (Courtesy Holley)


 

Volumetric efficiency is the volume of air the engine is theoretically capable of ingesting (potential) versus the actual volume that makes it into the cylinder, all other factors considered. In effect, it is the difference between the mass of the charge consumed by the cylinders and the mass of an equal volume at atmospheric pressure at any given RPM. It is affected by carburetor or throttle body size restrictions, engine speed, air temperature, manifold and port restrictions, valve size, chamber shrouding, camshaft overlap, and pumping losses.

Airflow measured on a running engine divided by the potential or theoretical air capacity at any given RPM is the engine’s actual volumetric efficiency at that particular engine speed. While not perfectly linear, it is sufficient for calculating volumetric efficiency. The following formula yields the percentage of volumetric efficiency:

VE % = (measured CFM ÷ potential CFM) x 100

If our 350-ci sample engine is a street engine and we are able to measure airflow on a dyno we might find that the actual airflow at 5,300 rpm is only 450 cfm and rising to 539 cfm at the maximum engine speed of 6,500 rpm. This would yield volumetric efficiency calculated as follows:

VE % = (450 ÷ 536) x 100 = 84% at the torque peak
VE % = (539 ÷ 658) x 100 = 81.9% at maximum engine speed
 
MuscleCarB

VE is an indicator of how well the induction system does its job of filling the cylinders. Millions of dyno pulls and extensive research have established typical VE percentages for most engines. Standard passenger cars are generally 70- to 80-percent efficient, while high performance engines range from the low 80s to the mid 90s. Tuned racing engines routinely exceed 100-percent volumetric efficiency because their high-flow cylinder heads, tuned intake systems, cam timing, and exhaust scavenging provide exceptional efficiency. Highly refined Pro Stock drag racing engines are capable of achieving up to 125-percent VE. That means that the actual charge in the cylinder is 25 percent denser than the same volume before it enters the engine. Combined with ultra-high compression ratios, it really packs some power in the form of mean effective pressure.

At 85-percent VE, a 350-ci street engine only consumes 297.5 ci of air by volume. The only way to change it is to supercharge it or increase the efficiency of cylinder filling by applying the right combination of naturally aspirated components. In a naturally aspirated engine the goal is to increase the inertia of the incoming charge and reduce the restrictions it has to navigate on its way to the cylinder. A good system accomplishes this with a mean port speed of about 240 ft/sec. The important thing to remember is that low restriction and high charge inertia are achievable through proper carburetor or throttle body sizing, appropriate manifolding and cylinder head port volumes that match engine displacement and anticipated RPM.

 

Power and Volumetric Efficiency

The cornerstone of power building is volumetric efficiency (VE). The more air an engine is able to process, the greater its power potential. Volumetric efficiency is determined according to an engine’s static air capacity or displacement. A displacement of 400 ci represents 100 percent air capacity for an engine of that particular size. At any given engine speed a percentage of that volume is being processed into torque, depending on a host of variables that conspire to limit airflow. Without these pesky restrictions, atmospheric pressure can easily fill the cylinders 100 percent every two crankshaft revolutions. In practice, this is difficult to achieve because airflow is restricted by a throttling device (carburetor, throttle body, or other), imperfect intake manifolding, intake ports, valves, and all the attending flow restrictions and pressure dynamics present in a running engine. Hence, VE in a production engine rarely exceeds 70 to 80 percent.  

As previously noted, VE is reduced below the torque peak due mainly to insufficient airflow and poor mixture quality. Above the torque peak, VE is limited by inadequate time to fill the cylinder due to RPM. One of the successful engine builder’s primary goals is to exceed the static air capacity of the engine and optimize combustion efficiency once fuel is introduced to the process. Savvy engine builders skillfully manipulate the component composition to accomplish this—broadening the torque curve and positioning it to best suit the intended application. 

In specifying components to meet VE requirements, builders target intake ports, dimensional qualities of intake manifolds and exhaust headers, carburetor size, rod-to-stroke ratios, valve timing, and static compression ratio. The specific component matrix is adjusted to suit the application’s operational requirements. Ovaltrack and road-racing engines typically call for a component mix producing a broad torque curve over a wide range of RPM. This affords the engine builder an opportunity to tune the intake and exhaust systems separately to effectively broaden the power band. Conversely, drag racing applications seek a higher and narrower power band in which intake and exhaust tuning are more closely aligned.   

Identifying and targeting the required power band is one of the engine builder’s first steps. Since VE and engine speed are closely aligned, it is critical to target VE modifications to the desired engine speed. If a drag racing engine leaves the starting line at 7,000 rpm and cycles between there and 9,000 rpm through the gears, its VE at 5,000 rpm is largely irrelevant. And, of course, an engine delivering power between 4,500 rpm and 7,200 rpm will need broader tuning efficiency from its parts combination. Hence, airflow management within the targeted engine speed range becomes a central challenge in matching or exceeding an engine’s potential VE capacity.
 

Intake Manifolds

Intake manifold and carburetor restrictions are prevalent in many types of racing. They are primarily intended to limit airflow and RPM potential. In some cases more than one choice is offered and the final selection is based on which configuration generates the best VE and torque tuning potential. That’s why, where rules permit, a twincarb high-RPM tunnel ram is chosen over a single 4-barrel for a drag racing application, but you’re not likely to see a tunnel-ram intake on a road racing car. Some classes dictate the use of a dual-plane intake, which often extends to the use of a stock cast-iron manifold. When the intake manifold is specified, all you can do is identify the manifold’s characteristics and tailor your package accordingly. 

We’ll also discuss how to map manifold characteristics on a flow bench to obtain a ballpark view of individual port strengths and weaknesses. Once you have a clear picture of the manifold’s efficiency you can evaluate potential steps to ensure its contribution to maximum performance. Depending on other restrictions, these may include rocker ratio or cam timing adjustments to individual cylinders based on individual runner flow dynamics. Or it may be addressed by manipulation of header dimensions to complement and possibly broaden the torque range dictated by the intake manifold’s fixed dimensions. If allowed, carb spacers may support better mixture quality and, in the case of dual-plane intakes, staggering jetting from side to side may also provide some improvement particularly as it relates to the lean side of the engine. Many circle track classes also require a 2-barrel carburetor of a specified size with no modifications allowed, although repositioning of the carburetor location on the intake manifold is sometimes permitted.  
 

Street Carburetor vs Race Carburetor

  Engine air capacity and VE are important to carburetor selection because most carburetor functions are initiated and controlled by airspeed through the venturis and boosters. Once you establish the engine’s airflow capacity using the CFM formula, you need to multiply it by the appropriate percentage to account for VE losses.   Street Carburetors   The general rule for performance street engines is 85 percent of the theoretical or potential air capacity.   Carb Sizecfm = [(displacement x RPM) ÷ 3,456] x 0.85   Recalling our theoretical 350-ci engine, we can calculate the cfm requirement at maximum engine speed:   CFM = [(350 x 6,500) ÷ 3456] x 0.85 = 559.5
 

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Carburetor venturi size also affects carburetor airflow capacity. Compare the 11⁄4-inch primary venturis on this 390-cfm Holley carburetor to the 13⁄8-inch primaries on a 750-cfm Holley HP 4-barrel. Note the degree of restriction caused by the smaller venturis on the 390 version. (Courtesy Holley)


 
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This Dominator is plenty of carburetor for a hot big-block engine, but it would perform poorly on most small-blocks except perhaps larger strokers such as World Products 454-ci small-block Chevy. (Courtesy Holley)


 
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To calculate equivalent throttle bore area, find the area of a single bore as shown here, then multiply it by the number of bores in your carburetor or throttle body.


 

The airflow demand at peak power is only 560 cfm, so a relatively small carburetor suits it well. Depending on the venturi and throttle plate size, a 550-cfm carburetor provides surprisingly crisp throttle response on the street. You are in the ballpark with a 600-cfm carb as well and, since most performance carburetor sizes start at 600 cfm, a 600- or 650-cfm carburetor gives you some wiggle room if you intend to make additional performance modifications later.  

Be aware that most manufacturers use a pressure drop of 3.0 inches of mercury (Hg) to rate 2-barrel carburetors and 1.5 in/Hg to rate 4-barrel carbs. These figures assume a maximum achieved vacuum at WOT under full load. In theory, an engine does not achieve a higher vacuum, but in practice they often do and that is generally an indication of the need for the next larger size of carburetor. You can check this in your own vehicle using a manifold vacuum gauge reading at wide-open throttle (WOT) on a drag strip. If your gauge reads more than 1.5 to 1.7 inches of vacuum under full load in high gear, your carburetor may be too small to deliver maximum performance at peak power.  
 

Race Carburetors

The general rule for racing carburetors is to have 1.1 times the calculated air demand because VE is usually greater than 100 percent. To accommodate the higher efficiency, multiply the theoretical air potential by 1.1. So if our 350 engine is highly modified with racing heads, cam, and intake manifold, we calculate as follows:  
Race Carbcfm = [(350 x 6,500) ÷ 3,456] x 1.1 = 724  

In this case, you would probably choose a 750-cfm carburetor since it is the nearest common size, especially if you are drag racing. If you are road racing, you might consider a 700-cfm Holley because it has 1/16-inch-smaller venturis that might improve throttle response off of tight corners. In this case the smaller carb may prove to be the better choice. As a general rule, it has been found that going with the smaller carb almost always yields the best results.   

Performance carburetors are mostly made in 50-cfm increments, so if your airflow calculations happen to split the difference, choose the smaller carb unless you have a compelling reason to go larger. Supercharger and turbocharger applications present a higher air demand to handle the increased airflow capacity of the supercharging device. (See “Boost and Supercharger Drive Ratios” on page 72.)  
 

Choosing Throttle Body Size

Throttle body equivalents pretty much parallel carburetor sizing because the engine’s airflow requirement is unchanged. In most throttle body applications the air is not burdened with the task of carrying fuel to the valve, but it still needs to maintain sufficient energy (velocity) to support efficient cylinder filling. To calculate an equivalent throttle body size based on known carburetor size, you need to recall the formula for the area of a circle:  

A = diameter2 x 0.7854  
Or, in this case:  
A = diameter2 x 0.7854 x number of throttle bores  

You can use this formula to calculate the throttle bore area of a given carburetor and compare it to an equivalent throttle body. You can calculate the area of a large single throttle body or the combined area of a multiple bore throttle body. Calculate the separate areas and multiply by the number of bores in the carburetor or throttle body.
 

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Two appropriately sized Holley 4-barrels ensure an adequate supply of air when the supercharger ramps up its air demand. (Courtesy Holley)


 
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Centrifugal blowers such as this procharger setup come on stronger with increased RPM and compressor speed. Swapping to a smaller pulley on the blower can raise the boost for a little weekend warrior activity. During the week you simply swap back to the larger pulley for daily driving. (Courtesy ATI )


 
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Many nitrous applications also require substantial carburetor support to ensure maximum performance. Even though you are adding extra oxygen chemically, the engine will respond better with larger carburetors. (Courtesy Holley)


 
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This 1,600-hp, 299-ci Ken Duttweiler–built Chevy is one angry small-block. Built exclusively for George Poteet’s 435-mph Bonneville streamliner, it is a model of mathematical efficiency with a properly sized single turbocharger.


 
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Turbocharger compressor maps are used to select the correct turbocharger based on calculated pressure ratios and the calculated mass air flow in pounds per minute for the horsepower requirement. The efficiency islands on the map indicate various levels of the efficiency range for that particular turbine housing. The point where the pressure ratio and the calculated air mass meet on the map shows the efficiency the turbine will achieve based on those parameters. (Courtesy Turbonetics)


 

Here’s an example with a 750 Holley carburetor that has four throttle bores measuring 17⁄16 inches compared to a single-bore 75-mm aftermarket throttle body for a fuel injected application:

First, find the total throttle area of the Holley.
Convert to decimals.
17⁄16 = 1.4375 inch
Find the area.
A = 1.43752 x 0.7854 x 4 = 6.49 square inches
Calculate the area of the 75-mm throttle body.
First convert to inches (multiply 75 mm by the conversion factor 0.0393701).
75 mm x 0.0393701 = 2.9527 inches (equivalent diameter)
Now calculate the area of the 2.9527-inch-diameter throttle bore.
2.95272 x 0.7854 = 6.84 square inches

Recall that the 750 cfm Holley had 6.94 square inches of throttle area, so the 75-mm throttle body is a little larger. To calculate an exact throttle body equivalent use a shortcut by working in percentages. It will get you very close.

6.49 (Holley) ÷ 6.84 (throttle body) = 94.8%
75 mm x 0.94 = 70.5 mm
A 70- or 72-mm throttle body would be the closest equivalent for your application. 
 

Calculating Supercharger Carburetor Size

Under boosted conditions, your supercharged engine requires up to 50-percent-more airflow capacity than a naturally-aspirated engine of equivalent displacement. Not discounting the air cleaner, the carburetor is the primary source of restriction for air entering the supercharger and, ultimately, the engine. The carburetor must be capable of serving the increased airflow demand and the additional fueling requirement under boost. Final air demand depends upon engine characteristics such as manifold and cylinder head efficiency (both VE contributors) and the amount of boost your supercharger is supplying. The calculation is based on engine speed, displacement, and the maximum anticipated boost pressure at WOT.

The following formula calculates the appropriate air demand and corresponding carburetor or throttle body size for your application:

CFMmax = (displacement x RPM ÷ 3,456) x [(max boost / 14.7) + 1]
Where:
RPM = max anticipated engine speed
Boost = maximum boost at WOT
14.7 = normal atmospheric pressure at sea level 
For example for a 302 Ford making 6 psi boost at 6,000 rpm: 
CFM = (302 x 600 ÷ 3456) x [(6 ÷ 14.7) + 1] = 524.3 x 1.4089 = 738 

Note that the VE correction factor (0.85) is conspicuously absent from the formula. In theory it shouldn’t be because the same restrictions that limit absolute VE in a normally aspirated engine are still present in your supercharged engine, and anything you do to decrease them will aid the efficiency of your supercharger. Most people contend that boost pressure overcomes these restrictions, and in practice it does to a degree, but it still has to perform the work and without the restrictions it will be more efficient. 

A similar formula used by many turbo manufacturers also ignores the VE correction. A logical explanation might be that both formulas provide a fudge factor to prevent users from undersizing the carburetor on their engines and thus making the supercharger or turbocharger appear less efficient. While the supercharging device may have enough dynamic range to overcome restrictions, it still introduces undesirable heat to the compressed charge resulting in boost pressure, but not necessarily an increase in air density. If the carburetor acts as a restriction and you drive the blower faster to overcome VE losses, the pressurized air may also gain so much heat that it exceeds the octane rating of your fuel.
 

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The turbine housing (in red) shows the actual location of the tongue (arrow) where the A/R ratio is measured in the volute. (Courtesy Turbonetics)


 
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The A/R ratio is the square area of the turbine housing volute at the end of the tongue divided by the radius from the center of the turbine wheel to the dynamic center (called the Centroid) of the gas flow path through the volute. (Courtesy Turbonetics)


 
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The A/R ratio also applies to the turbine or exhaust side of the turbocharger as indicated here by the arrow and oval on the exhaust turbine housing. (Courtesy Turbonetics)


 

VE-corrected formulas calculate the correct air requirement, but you can’t go wrong with the uncorrected formula because it ensures that your carburetor will never be a restriction. (If you want to incorporate the VE correction factor into your calculation, simply multiply the result by 0.85 for street carbs.) 

Note also that this calculation is for a carburetor used on the inlet side of the supercharger, such as in a Rootstype blower. It is not valid nor should it be used for a blow-through application. Also it should be noted that using this calculation doesn’t take into account the fact that Roots blowers are not very efficient and, as such, demand that the inlet side be as unrestricted as possible. That’s why you see dual carbs on most Roots blowers unless they are very mild street blowers. For a max-effort Roots blower, the inlet side must be left as unrestricted as possible; hence, two very large and oversized carbs. So this math should only be used for single-digit boost applications on mild engines where peak power is not the primary goal. 

The recommended method for calculating turbocharger carburetor size is based on a simple air mass calculation related to horsepower. Turbocharger manufacturers use the 10:1 rule which states that it takes one pound of air to make 10 hp. That pound of air varies in density according to the gas laws governing pressure, temperature, and volume, but the 10:1 ratio is relatively constant. 

Calculating the air mass in pounds per minute (lbs/min) provides a convenient way of figuring carburetor size. Divide the anticipated HP by 10: 500 hp divided by 10 equals an air mass requirement of 50 lbs/min. The engine must flow 50 pounds of air per minute to make 500 hp. 

Corrected Mass Air Flow = HP ÷ 10
500 hp ÷ 10 = 50 lbs/min
To convert the calculated air mass to CFM, divide by the standard air density factor 0.0691.
CFM = calculated mass air flow ÷ standard air density factor (0.0691)
CFM = 50 lbs/min ÷ 0.0691 = 723.6
This assumes 100-percent VE so don’t forget to correct by the VE correction factor of 0.85.
723.6 x 0.85 = 615 cfm

If this seems too small it is—because you still have to multiply by the density ratio, which is read from density ratio charts based on efficiency ratios for various turbochargers. In our example we discovered a density ratio of 1.25 for a turbocharger with a 74-percent efficiency ratio.

723.6 x 1.25 = 905 cfm

In practice you should consult with the turbocharger manufacturer who will help match your carburetor selection to the corresponding turbocharger based on the turbocharger’s pressure ratio and the appropriate air density for the boost you will be running. 

Sizing a Turbocharger The formula for calculating turbocharger boost pressure ratios provides a convenient means of selecting the proper turbocharger compressor wheel by plotting the calculated pressure ratio against the previously mentioned mass air calculation in lbs/min on a turbocharger compressor map. 

Pressure Ratio = max boost + ambient pressure (usually 14.7) ÷ ambient pressure (usually 14.7)

Example: If we assume a max boost pressure of 6 psi, we calculate as follows: 
 

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The smaller A/R shown on the right improves turbine response time so the turbo builds boost more quickly. The larger volute on the left is designed to build big power at higher RPM. (Courtesy Turbonetics)


 
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The relationship of the blower pulley (driven) diameter and tooth count to that of the crank (drive) pulley is the blower drive ratio. When the ratio is positive (crank pulley larger), the blower is overdriven. When the crank pulley is smaller the ratio is negative or underdriven and the blower runs slower than crank speed. (Courtesy Weiand)


 
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Modern mini-blowers such as this Weiand system run at higher RPM than traditional Roots blowers, but the drive ratio is still controlled by pulley size. In most cases only the upper pulley is changed to raise or lower the boost. (Courtesy Weiand)


 
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The chart above is for a Weiand 6-71 blower with 8-mmpitch drive pulleys. It illustrates how one pulley can be changed to achieve a specific blower speed.


 
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This chart shows the static and effective compression ratio at various boost levels for both pump gas and race gas. The line through the center delineates the practical limit for most pump-gas applications. (Courtesy Weiand)


 
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This chart shows estimated boost levels for common drive ratios and engine sizes. (Courtesy Weiand)


 
Pressure Ratio = (6 + 14.7) ÷ 14.7 = 1.408  

Most turbocharger manufacturers publish their compressor maps and density ratio charts online for your convenience. To select an appropriate compressor, you refer to the turbocharger compressor map that plots the corrected mass air flow in lbs/min on the horizontal axis and the calculated pressure ratio on the vertical axis. (The irregular shaped lines in the center that look like a geologist’s terrain map are called efficiency islands. They indicate the effective range of a given compressor’s efficiency at various pressure ratios and mass air flow levels.)   

To use the compressor map you read horizontally from the previously calculated pressure ratio until you meet the vertical line rising from the mass airflow in pounds per minute. The point where they cross will fall somewhere on one of the indicated efficiency islands. For a street application you want a minimum of 65- to 70-percent efficiency and it’s not usually difficult to find a compressor that will put you in the 72- to 74-percent range. Here again it is fun to brainstorm compressor maps and efficiency ratios, but for best results, work with your turbocharger manufacturer to select the best turbine for your particular application and anticipated usage. If you’ve done your calculations carefully, you might even be surprised to find that they approve of your preliminary selection.
 

Boost and Supercharger Drive Ratios

The amount of boost your supercharger delivers depends on its size and efficiency and the speed that you drive it relative to the crankshaft. The crankshaft is the “drive” or driven device and the supercharger is the “driven” device. Your ability to adjust supercharger boost is controlled by the supercharger drive ratio, which is the relationship between the size and tooth count on the drive pulley relative to that of the blower or driven pulley. Before you consider increasing the boost, keep in mind that higher boost levels do not necessarily produce denser air for the engine to process. Depending on your combination, it may simply result in hotter air at higher pressure but no real increase in useful oxygen content. For this reason large increases in boost are ill advised unless you can supplement them with effective charge cooling or higher octane fuel.
 

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This chart shows estimated boost levels for common drive ratios and engine sizes. (Courtesy Weiand)


 

Supercharger speed is determined by the blower drive ratio. If the drive pulley and the driven pulley both have the same tooth count, the drive ratio is 1:1 and the blower turns at the same speed as the crankshaft. If the crank (drive) pulley is larger than the blower (driven) pulley, the blower is overdriven by the relative percentage. If the blower pulley is larger than the crank pulley the blower is underdriven. Use the following formulas to calculate the percentage of overor underdrive based on pulley size (tooth count):

% Overdrive = tooth count, driven pulley (blower) ÷ tooth count, drive pulley (crank) 
% Underdrive = tooth count, drive pulley (crank) ÷ tooth count, driven pulley (blower) 

To estimate supercharger speed at any given engine speed, multiply the engine speed by the current blower drive ratio. 
Supercharger Speed = RPM x blower drive ratio

If you have a supercharger pulley arrangement where the blower is overdriven by a ratio of 1.1 (10 percent) and the maximum engine speed is 6,500 rpm, the blower speed is 7,150 rpm. 

Supercharger Speed = 6,500 x 1.1 = 7,150 rpm 

Supercharger manufacturers publish their supercharger drive ratios and corresponding boost levels in charts that show the tooth count and percentage of over- or underdrive. These charts indicate the amount of boost you can expect from a given ratio relative to the displacement of your engine. 

For example, a Weiand 6-71 blower driven 1:1 delivers 8.5 pounds of boost on a 454-ci engine. You can raise that to 9.6 pounds by overdriving the blower 5 percent (1.056 times crank speed). The accompanying charts indicate the appropriate pulley relationship to achieve the desired boost level. 

If you need to lower the boost to avoid detonation, you can underdrive the blower 5 percent (0.95 times crank speed) to get 7.3 pounds. Usually you only have to change one pulley, or swap upper and lower pulleys to achieve your goal. 

Overdrive percentages on the older style 6-71 and 8-71 blowers rarely exceed 30 percent, but note that the more recent mini-blowers and centrifugal blowers are driven much faster; more than double crank speed in some cases. You have to pay careful attention to these blowers, especially the centrifugal type, because they can easily exceed boost limits at higher engine speeds. Consult the manufacturer’s published drive ratios and boost charts to match your particular application.
 

Wave Tuning

We tend to think of intake flow as the smooth, steady passage of an air/fuel mixture through an intake port and into a cylinder, but the dynamics are far more complicated. Engineers have long recognized the effects of wave tuning within the inlet system, but until recently it was never deemed necessary or cost effective to pursue it in production vehicles. Racers have known about it for a long time as evidenced by the racing efforts of the Ramchargers in the late 1950s and early 1960s. Various racing efforts have made good use of wave tuning over the years. What we find in the inlet tract is a continuous series of starts and stops as the intake valve opens and closes. Within this physical stream of flow, supersonic pulses are reflected back and forth between the cylinder and the atmospheric source of inlet flow. These are high- and lowpressure pulses depending on the point of origin. The intake flow has inertia, which creates a low-pressure pulse reflected from the intake valve every time it opens. This reverse pulse travels back toward the inlet entry much faster than, and right through, the still onrushing gas mixture until it reaches the inlet entry or atmospheric pressure. At that point a positive high-pressure pulse is reflected back toward the valve. The reflected pulse travels down the inlet tract until it reflects off the piston top as another high-pressure pulse traveling back toward the entry again. This time the inlet entry reflects it back as a low-pressure pulse and the cycle begins again. Within this series of alternating high-speed pulses we can make good use of the incoming highpressure pulses to increase the density of the fuel charge by using its energy to effectively boost more molecules into the cylinder.

Dyno tests with individual runner (IR) manifolds have shown significant power gains when the lengths of the intake stacks are carefully matched to take advantage of pulse timing. The trick is to match camshaft timing and inlet tract length so that a high-pressure pulse arrives just as the valve opens and sweeps additional mixture into the cylinder.

The speed of a pulse through an air/fuel mixture varies with its temperature, but for calculation purposes it is most often related as 1,100 ft/sec at 100 degrees F, which is representative of real-world temperatures. Pulse timing is controlled by the speed of the pulse, the length of the inlet path, and the timing of intake valve event. Since valve operation and pulse speed are fixed, the length of the inlet can be tuned to achieve resonance at some particular engine speed that we can take advantage of.

In the 1960s, Chrysler engineers established a mathematical constant (K-value) which enabled them to calculate the optimum intake length within a range of plus-or-minus 3 inches. While that seems a bit vague, it is also known that some benefit begins to accrue on either side as engine speed approaches the “sweet spot.” This point of resonance is calculated as follows:
L = [(K x C) ÷ N] + 3
Where: L = length of the inlet path in inches
K = mathematical constant (Chrysler chose 72)
C = speed of the pulse (arbitrary according to temperature)
N = engine speed (RPM) ± = recommendation to encourage experimentation to determine the actual “sweet spot”

So for a given engine speed of, say, 6,000 rpm, we can calculate an optimum inlet path length.
L = [(72 x 1,100) ÷ 6,000] ± 3 L = 12 ± 3 inches

This would be the ideal length from the intake valve to the inlet entry for atmospheric pressure. Performance author Phillip Smith addresses this concept in his book Scientific Design of Exhaust and Intake Systems. His research derived a K-value of 90, which substantially increases the length requirement.

In the absence of more precise research (which undoubtedly exists within the engineering departments of major automakers), it is difficult to determine the ideal K-value. We know from experience that critically-tuned inlets deliver exceptional power when operated within the narrow range of their optimum engine speed. If a car’s transmission gears are selected to provide minimal RPM drop on each shift, the engine can be run within its peak efficiency range most of the time. This is reinforced by factory efforts to investigate and implement variable-length inlet systems, and by the fact that almost all OEM performance engines make use of very precise inlet-length tuning like that found on third-generation GM LS series small-blocks and recent Chrysler Hemis.

It is more difficult to apply this in practice because aftermarket intakes are manufactured to a fixed length, but you might think about why tunnel ram manifolds are so effective at high-RPM ram tuning, particularly above 7,000 rpm. Take a look at any Pro Stock intake (if it’s not covered up) and you’ll see runners optimized for the high- RPM Pro Stock engine environment. The higher the RPM, the shorter the runner. Another critical factor is runner taper (typically about 4 degrees), which is easily seen on most manifolds. The use of taper is beyond the scope of this book, but you can learn all about it with Motion Software’s Dynomation program (download the manual for free at www.motionsoftware.com), which makes extensive use of wave tuning and taper for accurate engine simulation.

To some degree this thinking is partially evident in street intakes, like the high-torque Edelbrock Performer RPM, which employs lengthy constant cross-sectional area runners to boost torque. The runner length is, by necessity, an ideal compromise, but manufacturers have tried very hard to size these manifolds for optimum results knowing full well that they will be employed across a broad range of engine sizes and speeds. Their performance proves that they have done an exceptional job. On the other hand, if you’re running a 5-mile-long, high- RPM pull at Bonneville with an IR intake system, critical dyno testing can help you pinpoint the exact length to cut your stacks for optimum wave tuning in your desired RPM range. It’s food for thought and kind of fun, too.

Ram Effects and Inlet Cooling Many racers make use of a hood scoop to capture and direct more air into the carburetor(s). If properly configured with a sealed air box, it can provide a slight pressure boost that can increase power. It may also provide additional power due to the cooling effect of the high-speed air entering the air box.

First, consider the “ram air” effect of high-speed air entering the scoop and the air box. A good system has a sealed air box surrounding the carburetor entry. Depending on the layout, the scoop is often designed with a smaller opening that expands into the air box to help slow the air so it can make the turn into the carburetor(s). It’s well known that the shape of the scoop entry determines the degree of efficiency it provides. Scoops with straight cut edges are not very effective, but those with a generously curved radius can recover as much as 90 percent of the incoming air pressure, which of course increases with the car’s velocity. The following formula is used to calculate the pressure increase provided by ram air assuming a nicely curved entry radius and 90 percent pressure recovery.

Pvel. = (V2 x p) ÷ 4,311
Where: Pvel. = velocity-induced pressure increase
p = standard air density
V= vehicle speed in mph
4,311 = mathematical constant

If we assume standard air density of 0.0691 we can calculate the pressure increase according to the speed of the vehicle. In this case we’ll assume a drag car that achieves 165 mph by about the 1,000-foot mark.

Pvel. = (1652 x 0.0691) ÷ 4,311 = 0.436 psi

That assumes perfect pressure recovery, which is virtually impossible, so we’ll add a pressure recovery factor of 90 percent, assuming our scoop has a well-rounded inlet radius.

Pvel. = (165 x 0.0691 x 0.90) ÷ 4311 = 0.392 psi

That’s about four tenths of a pound positive pressure at the carburetor. To calculate the percentage of power increase it might provide, we can refer to standard atmospheric pressure:

% increase = (14.7 + 0.392) ÷ 14.7 = 1.026

That’s roughly 21⁄2 percent, or 15 hp, on a 600-hp car. To quantify this you could use a data acquisition system with a pressure sensor located in the scoop. Since the system also records time and speed, you can log the scoop’s pressure recovery efficiency throughout an entire run as speed and air pressure increase.

Depending on engine speed, air temperature, and the efficiency of your induction system, you may also achieve a slight cooling effect by increasing velocity through the carburetor. If, through data logging you can determine that the incoming air temperature is 100 degrees F and the temperature in the manifold plenum drops to 88 degrees F due to velocity cooling, you can calculate the potential power gain provided by the denser air. To do so, you have to add the recorded temperature to degrees Kelvin.

V1 = (plenum temp + 459.4) ÷ (inlet temp + 459.4)
V1 = (88 + 459.4) ÷ (100 + 459.4) = 0.978
To convert the new air density, divide 1 by 0.978. 1 ÷ 0.978 = 1.02

So, the cooling effect could supply 2-percent-denser air. And since power is related to air mass flow per minute, you can expect a power increase of roughly 2 percent from inlet cooling. That’s an additional 10 to 12 hp on a 600-hp engine. Again, it is difficult to quantify all of this without accurate data logging to compare against track performance, which would most easily be seen as increased trap speed. To further evaluate it you may want to plug off the scoop or run a flat hood if possible so the engine breathes underhood air temperature with no pressure increase. And you also have to consider the aerodynamic drag of the scoop, which may offset some of the gain from ram air pressure and airspeed cooling. It’s always something!
 
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How to Calculate Runner Cross Section

As noted earlier, intake runner cross section is a primary influence of torque peak location within the engine’s power band. If you’re inclined to calculate such things it can be difficult because manufacturers do not publish this information; indeed, some of them may not even know it themselves. It’s well known that Edelbrock’s Performer RPM dual-plane intake features constant crosssection runners. And there is no doubt that Edelbrock has sized the runners for optimum performance across the normal street operating range. The constant cross section ensures consistent runner velocity, which discourages air/fuel separation. Because air and fuel molecules differ in weight, they are susceptible to separation when the mixture experiences velocity changes according to variations in cross section or abrupt changes in direction. Edelbrock’s diligence in this regard is a primary reason why the Performer RPM is one of the most potent and popular dual-plane intakes available.

 

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To calculate the average intake-runner cross section, measure the height and width of the runner entry and exit with dial calipers. The entry and exit are usually different so take the average of the two cross sections.


 

Still, those who wish to determine the average cross section of an unknown intake runner can achieve a close approximation by carefully measuring the dimensions of the runner inlet in the plenum and the runner exit at the manifold/cylinder head flange. Using the appropriate size telescoping gauge (snap gauge), measure the runner inlets at a point far enough down the runner to avoid a false reading at the rounded runner entry. Calculate the cross section there and at the runner exit and average the two to get the mean cross section of the runner. This is sufficient for calculating a torque peak value for the purpose of comparison with other intakes and is, of course, independent of any air/fuel separation issue that may exist in some manifolds due to sharp runner turns or inconsistent velocity caused by area variations.

Knowing the cross section allows you to predict the torque peak RPM, but you still can’t adjust it with a fixed manifold casting. You can partially influence it to the degree that you can broaden it via complementary adjustments to the header primary pipe cross section, which is easier to change. Calculate the torque peak RPM:

Torque Peak RPM = runner cross section x 88,200 ÷ individual cylinder volume

Then reverse the formula to calculate a header cross section that promotes a secondary peak to broaden the curve.

Cross Section = Peak torque RPM x cylinder volume ÷ 88,200

While not exact, this method can help you ballpark a header selection that effectively complements your fixed area intake manifold. If you wish to pursue it further, consider the difference in intake runner lengths within the same manifold. Since runner length tends to rock the torque curve about the torque peak, you may be able to use changes in selected primary pipe header lengths to complement individual runner lengths in the manifold.

Written by John Baechtel and Posted with Permission of CarTechBooks

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