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Gasoline FAQ - Part 3 of 4

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Subject: 6. What do Fuel Octane ratings really indicate?

6.1  Who invented Octane Ratings?

Since 1912 the spark ignition internal combustion engine's compression ratio 
had been constrained by the unwanted "knock" that could rapidly destroy 
engines. "Knocking" is a very good description of the sound heard from an 
engine using fuel of too low octane. The engineers had blamed the "knock" 
on the battery ignition system that was added to cars along with the 
electric self-starter. The engine developers knew that they could improve 
power and efficiency if knock could be overcome. 

Kettering assigned Thomas Midgley, Jr. to the task of finding the exact 
cause of knock [24]. They used a Dobbie-McInnes manograph to demonstrate 
that the knock did not arise from preignition, as was commonly supposed, but
arose from a violent pressure rise *after* ignition. The manograph was not
suitable for further research, so Midgley and Boyd developed a high-speed 
camera to see what was happening. They also developed a "bouncing pin" 
indicator that measured the amount of knock [9]. Ricardo had developed an
alternative concept of HUCF ( Highest Useful Compression Ratio ) using a 
variable-compression engine. His numbers were not absolute, as there were 
many variables, such as ignition timing, cleanliness, spark plug position, 
engine temperature. etc.
In 1927 Graham Edgar suggested using two hydrocarbons that could be produced 
in sufficient purity and quantity [11]. These were "normal heptane", that 
was already obtainable in sufficient purity from the distillation of Jeffrey 
pine oil, and " an octane, named 2,4,4-trimethyl pentane " that he first 
synthesized. Today we call it " iso-octane " or 2,2,4-trimethyl pentane. The 
octane had a high antiknock value, and he suggested using the ratio of the 
two as a reference fuel number. He demonstrated that all the commercially- 
available gasolines could be bracketed between 60:40 and 40:60 parts by 
volume heptane:iso-octane.

The reason for using normal heptane and iso-octane was because they both 
have similar volatility properties, specifically boiling point, thus the 
varying ratios 0:100 to 100:0 should not exhibit large differences in 
volatility that could affect the rating test.
                                                           Heat of
               Melting Point  Boiling Point  Density    Vaporisation
                     C              C          g/ml         MJ/kg
normal heptane    -90.7           98.4       0.684          0.365 @ 25C
iso octane       -107.45          99.3       0.6919         0.308 @ 25C

Having decided on standard reference fuels, a whole range of engines and
test conditions appeared, but today the most common are the Research Octane
Number ( RON ), and the Motor Octane Number ( MON ).

6.2  Why do we need Octane Ratings?

To obtain the maximum energy from the gasoline, the compressed fuel-air 
mixture inside the combustion chamber needs to burn evenly, propagating out 
from the spark plug until all the fuel is consumed. This would deliver an 
optimum power stroke. In real life, a series of pre-flame reactions will 
occur in the unburnt "end gases" in the combustion chamber before the flame 
front arrives. If these reactions form molecules or species that can 
autoignite before the flame front arrives, knock will occur [21,22].
Simply put, the octane rating of the fuel reflects the ability of the 
unburnt end gases to resist spontaneous autoignition under the engine test
conditions used. If autoignition occurs, it results in an extremely rapid 
pressure rise, as both the desired spark-initiated flame front, and the 
undesired autoignited end gas flames are expanding. The combined pressure 
peak arrives slightly ahead of the normal operating pressure peak, leading 
to a loss of power and eventual overheating. The end gas pressure waves are 
superimposed on the main pressure wave, leading to a sawtooth pattern of 
pressure oscillations that create the "knocking" sound.

The combination of intense pressure waves and overheating can induce piston 
failure in a few minutes. Knock and preignition are both favoured by high 
temperatures, so one may lead to the other. Under high-speed conditions 
knock can lead to preignition, which then accelerates engine destruction 

6.3  What fuel property does the Octane Rating measure?

The fuel property the octane ratings measure is the ability of the unburnt
end gases to spontaneously ignite under the specified test conditions.
Within the chemical structure of the fuel is the ability to withstand  
pre-flame conditions without decomposing into species that will autoignite 
before the flame-front arrives. Different reaction mechanisms, occurring at
various stages of the pre-flame compression stroke, are responsible for the 
undesirable, easily-autoignitable, end gases.

During the oxidation of a hydrocarbon fuel, the hydrogen atoms are removed 
one at a time from the molecule by reactions with small radical species
(such as OH and HO2), and O and H atoms. The strength of carbon-hydrogen
bonds depends on what the carbon is connected to. Straight chain HCs such as
normal heptane have secondary C-H bonds that are significantly weaker than
the primary C-H bonds present in branched chain HCs like iso-octane [21,22].

The octane rating of hydrocarbons is determined by the structure of the 
molecule, with long, straight hydrocarbon chains producing large amounts of 
easily-autoignitable pre-flame decomposition species, while branched and 
aromatic hydrocarbons are more resistant. This also explains why the octane
ratings of paraffins consistently decrease with carbon number. In real life, 
the unburnt "end gases" ahead of the flame front encounter temperatures up 
to about 700C due to compression and radiant and conductive heating, and 
commence a series of pre-flame reactions. These reactions occur at different 
thermal stages, with the initial stage ( below 400C ) commencing with the 
addition of molecular oxygen to alkyl radicals, followed by the internal 
transfer of hydrogen atoms within the new radical to form an unsaturated, 
oxygen-containing species. These new species are susceptible to chain 
branching involving the HO2 radical during the intermediate temperature 
stage (400-600C), mainly through the production of OH radicals. Above 600C, 
the most important reaction that produces chain branching is the reaction of 
one hydrogen atom radical with molecular oxygen to form O and OH radicals.

The addition of additives such as alkyl lead and oxygenates can 
significantly affect the pre-flame reaction pathways. Antiknock additives 
work by interfering at different points in the pre-flame reactions, with
the oxygenates retarding undesirable low temperature reactions, and the
alkyl lead compounds react in the intermediate temperature region to 
deactivate the major undesirable chain branching sequence [21,22]. 

The antiknock ability is related to the "autoignition temperature" of the 
hydrocarbons. Antiknock ability is _not_ substantially related to:-
1. The energy content of fuel, this should be obvious, as oxygenates have 
   lower energy contents, but high octanes.
2. The flame speed of the conventionally ignited mixture, this should be
   evident from the similarities of the two reference hydrocarbons. 
   Although flame speed does play a minor part, there are many other factors 
   that are far more important. ( such as compression ratio, stoichiometry,
   combustion chamber shape, chemical structure of the fuel, presence of 
   antiknock additives, number and position of spark plugs, turbulence etc.)
   Flame speed does not correlate with octane.

6.4  Why are two ratings used to obtain the pump rating?

The correct name for the (RON+MON)/2 formula is the "antiknock index",
and it remains the most important quality criteria for motorists [39].

The initial knock measurement methods developed in the 1920s resulted in a 
diverse range of engine test methods and conditions, many of which have been
summarised by Campbell and Boyd [103]. In 1928 the Co-operative Fuel Research
Committee formed a sub-committee to develop a uniform knock-testing
apparatus and procedure. They settled on a single-cylinder, valve-in-head,
water-cooled, variable compression engine of 3.5"bore and 4.5" stroke. The
knock indicator was the bouncing-pin type. They selected operating conditions
for evaluation that most closely match the current Research Method, however
correlation trials with road octanes in the early 1930s exhibited such large 
discrepancies that conditions were changed ( higher engine speed, hot mixture
temperature, and defined spark advance profiles ), and a new tentative ASTM 
Octane rating method was produced. This method is similar to the operating 
conditions of the current Motor Octane procedure [12,103]. Over several 
decades, a large number of alternative octane test methods appeared. These 
were variations to either the engine design, or the specified operating 
conditions [103]. During the 1950-1960s attempts were made to internationally 
standardise and reduce the number of Octane Rating test procedures.

During the late 1940s - mid 1960s, the Research method became the important 
rating because it more closely represented the octane requirements of the 
motorist using the fuels/vehicles/roads then available. In the late 1960s 
German automakers discovered their engines were destroying themselves on 
long Autobahn runs, even though the Research Octane was within specification. 
They discovered that either the MON or the Sensitivity ( the numerical 
difference between the RON and MON numbers ) also had to be specified. Today 
it is accepted that no one octane rating covers all use. In fact, during 
1994, there have been increasing concerns in Europe about the high 
Sensitivity of some commercially-available unleaded fuels.

The design of the engine and vehicle significantly affect the fuel octane 
requirement for both RON and MON. In the 1930s, most vehicles would have 
been sensitive to the Research Octane of the fuel, almost regardless of the 
Motor Octane, whereas most 1990s engines have a 'severity" of one, which 
means the engine is unlikely to knock if a changes of one RON is matched by 
an equal and opposite change of MON [32]. I should note that the Research 
method was only formally approved in 1947, but used unofficially from 1942.

6.5  What does the Motor Octane rating measure?

The conditions of the Motor method represent severe, sustained high speed, 
high load driving. For most hydrocarbon fuels, including those with either 
lead or oxygenates, the motor octane number (MON) will be lower than the 
research octane number (RON).

Test Engine conditions                Motor Octane 
Test Method                         ASTM D2700-92 [104]
Engine                       Cooperative Fuels Research ( CFR )
Engine RPM                               900 RPM
Intake air temperature                    38 C
Intake air humidity           3.56 - 7.12 g H2O / kg dry air        
Intake mixture temperature               149 C 
Coolant temperature                      100 C
Oil Temperature                           57 C
Ignition Advance - variable     Varies with compression ratio
                                 ( eg 14 - 26 degrees BTDC ) 
Carburettor Venturi                       14.3 mm

6.6  What does the Research Octane rating measure?

The Research method settings represent typical mild driving, without
consistent heavy loads on the engine.

Test Engine conditions               Research Octane
Test Method                         ASTM D2699-92 [105]
Engine                       Cooperative Fuels Research ( CFR )       
Engine RPM                               600 RPM
Intake air temperature       Varies with barometric pressure 
                           ( eg 88kPa = 19.4C, 101.6kPa = 52.2C )
Intake air humidity           3.56 - 7.12 g H2O / kg dry air
Intake mixture temperature            Not specified 
Coolant temperature                      100 C
Oil Temperature                           57 C
Ignition Advance - fixed            13 degrees BTDC 
Carburettor Venturi           Set according to engine altitude          
                           ( eg 0-500m=14.3mm, 500-1000m=15.1mm ) 

6.7  Why is the difference called "sensitivity"?

RON - MON = Sensitivity. Because the two test methods use different test 
conditions, especially the intake mixture temperatures and engine speeds, 
then a fuel that is sensitive to changes in operating conditions will have 
a larger difference between the two rating methods. Modern fuels typically 
have sensitivities around 10. The US 87 (RON+MON)/2 unleaded gasoline is 
recommended to have a 82+ MON, thus preventing very high sensitivity fuels 
[39]. Recent changes in European gasolines has caused concern, as high 
sensitivity unleaded fuels have been found that fail to meet the 85 MON 
requirement of the EN228 European gasoline specification [106]. 

6.8  What sort of engine is used to rate fuels?

Automotive octane ratings are determined in a special single-cylinder engine 
with a variable compression ratio ( CR 4:1 to 18:1 ) known as a Cooperative 
Fuels Research ( CFR ) engine. The cylinder bore is 82.5mm, the stroke is 
114.3mm, giving a displacement of 612 cm3. The piston has four compression 
rings, and one oil control ring. The intake valve is shrouded. The head and 
cylinder are one piece, and can be moved up and down to obtain the desired 
compression ratio.  The engines have a special four-bowl carburettor that 
can adjust individual bowl air-fuel ratios. This facilitates rapid switching 
between reference fuels and samples. A magnetorestrictive detonation sensor 
in the combustion chamber measures the rapid changes in combustion chamber 
pressure caused by knock, and the amplified signal is measured on a 
"knockmeter" with a 0-100 scale [104,105]. A complete Octane Rating engine 
system costs about $200,000 with all the services installed. Only one 
company manufactures these engines, the Waukesha Engine Division of Dresser 
Industries, Waukesha. WI 53186.
6.9  How is the Octane rating determined?

To rate a fuel, the engine is set to an appropriate compression ratio that 
will produce a knock of about 50 on the knockmeter for the sample when the 
air-fuel ratio is adjusted on the carburettor bowl to obtain maximum knock. 
Normal heptane and iso-octane are known as primary reference fuels. Two 
blends of these are made, one that is one octane number above the expected 
rating, and another that is one octane number below the expected rating. 
These are placed in different bowls, and are also rated with each air-fuel
ratio being adjusted for maximum knock. The higher octane reference fuel 
should produce a reading around 30-40, and the lower reference fuel should
produce a reading of 60-70. The sample is again tested, and if it does not 
fit between the reference fuels, further reference fuels are prepared, and 
the engine readjusted to obtain the required knock. The actual fuel rating 
is interpolated from the knockmeter readings [104,105].  

6.10 What is the Octane Distribution of the fuel?

The combination of vehicle and engine can result in specific requirements
for octane that depend on the fuel. If the octane is distributed differently 
throughout the boiling range of a fuel, then engines can knock on one brand 
of 87 (RON+MON)/2, but not on another brand. This "octane distribution" is 
especially important when sudden changes in load occur, such as high load,
full throttle, acceleration. The fuel can segregate in the manifold, with 
the very volatile fraction reaching the combustion chamber first and, if 
that fraction is deficient in octane, then knock will occur until the less 
volatile, higher octane fractions arrive [27,28]. 

Some fuel specifications include delta RONs, to ensure octane distribution 
throughout the fuel boiling range was consistent. Octane distribution was 
seldom a problem with the alkyl lead compounds, as the tetra methyl lead
and tetra ethyl lead octane volatility profiles were well characterised, but 
it can be a major problem for the new, reformulated, low aromatic gasolines, 
as MTBE boils at 55C, whereas ethanol boils at 78C. Drivers have discovered
that an 87 (RON+MON)/2 from one brand has to be substituted with an 89
(RON+MON)/2 of another, and that is because of the combination of their 
driving style, engine design, vehicle mass, fuel octane distribution, fuel 
volatility, and the octane-enhancers used.
6.11 What is a "delta Research Octane number"?

To obtain an indication of behaviour of a gasoline during any manifold 
segregation, an octane rating procedure called the Distribution Octane 
Number was used. The rating engine had a special manifold that allowed 
the heavier fractions to be separated before they reached the combustion 
chamber [27]. That method has been replaced by the "delta" RON procedure. 

The fuel is carefully distilled to obtain a distillate fraction that boils 
to the specified temperature, which is usually 100C. Both the parent fuel 
and the distillate fraction are rated on the octane engine using the 
Research Octane method [107]. The difference between these is the delta 
RON(100C), usually just called the delta RON. The delta RON ratings are
not particularly relevant to engines with injectors, and are not used in
the US.   

6.12 How do other fuel properties affect octane?

Several other properties affect knock. The most significant determinant of 
octane is the chemical structure of the hydrocarbons and their response to 
the addition of octane enhancing additives. Other factors include:-
Front End Volatility - Paraffins are the major component in gasoline, and 
  the octane number decreases with increasing chain length or ring size, but 
  increases with chain branching. Overall, the effect is a significant 
  reduction in octane if front end volatility is lost, as can happen with 
  improper or long term storage. Fuel economy on short trips can be improved 
  by using a more volatile fuel, at the risk of carburettor icing and 
  increased evaporative emissions. 
Final Boiling Point.- Decreases in the final boiling point increase fuel 
  octane. Aviation gasolines have much lower final boiling points than 
  automotive gasolines. Note that final boiling points are being reduced
  because the higher boiling fractions are responsible for disproportionate
  quantities of pollutants and toxins. 
Preignition tendency - both knock and preignition can induce each other.

6.13 Can higher octane fuels give me more power?

On modern engines with sophisticated engine management systems, the engine
can operate efficiently on fuels of a wider range of octane rating, but there 
remains an optimum octane for the engine under specific driving conditions. 
Older cars without such systems are more restricted in their choice of fuel, 
as the engine can not automatically adjust to accommodate lower octane fuel.
Because knock is so destructive, owners of older cars must use fuel that will 
not knock under the most demanding conditions they encounter, and must 
continue to use that fuel, even if they only occasionally require the octane.  

If you are already using the proper octane fuel, you will not obtain more
power from higher octane fuels. The engine will be already operating at 
optimum settings, and a higher octane should have no effect on the management
system. Your driveability and fuel economy will remain the same. The higher 
octane fuel costs more, so you are just throwing money away. If you are 
already using a fuel with an octane rating slightly below the optimum, then 
using a higher octane fuel will cause the engine management system to move to
the optimum settings, possibly resulting in both increased power and improved
fuel economy. You may be able to change octanes between seasons ( reduce 
octane in winter ) to obtain the most cost-effective fuel without loss of 

Once you have identified the fuel that keeps the engine at optimum settings, 
there is no advantage in moving to an even higher octane fuel. The 
manufacturer's recommendation is conservative, so you may be able to 
carefully reduce the fuel octane. The penalty for getting it badly wrong, 
and not realising that you have, could be expensive engine damage. 

6.14 Does low octane fuel increase engine wear?

Not if you are meeting the octane requirement of the engine. If you are not
meeting the octane requirement, the engine will rapidly suffer major damage 
due to knock. You must not use fuels that produce sustained audible knock,
as engine damage will occur. If the octane is just sufficient, the engine 
management system will move settings to a less optimal position, and the 
only major penalty will be increased costs due to poor fuel economy. 
Whenever possible, engines should be operated at the optimum position for 
long-term reliability. Engine wear is mainly related to design, 
manufacturing, maintenance and lubrication factors. Once the octane and 
run-on requirements of the engine are satisfied, increased octane will have 
no beneficial effect on the engine. Run-on is the tendency of an engine to
continue running after the ignition has been switched off, and is discussed
in more detail in Section 8.2. The quality of gasoline, and the additive 
package used, would be more likely to affect the rate of engine wear, rather 
than the octane rating. 

6.15 Can I mix different octane fuel grades?

Yes, however attempts to blend in your fuel tank should be carefully
planned. You should not allow the tank to become empty, and then add 50% of 
lower octane, followed by 50% of higher octane. The fuels may not completely 
mix immediately, especially if there is a density difference. You may get a 
slug of low octane that causes severe knock. You should refill when your 
tank is half full. In general the octane response will be linear for most 
hydrocarbon and oxygenated fuels eg 50:50 of 87 and 91 will give 89. 

Attempts to mix leaded high octane to unleaded high octane to obtain higher 
octane are useless for most commercial gasolines. The lead response of the 
unleaded fuel does not overcome the dilution effect, thus 50:50 of 96 leaded 
and 91 unleaded will give 94. Some blends of oxygenated fuels with ordinary 
gasoline can result in undesirable increases in volatility due to volatile 
azeotropes, and some oxygenates can have negative lead responses. The octane 
requirement of some engines is determined by the need to avoid run-on, not 
to avoid knock.

6.16 What happens if I use the wrong octane fuel?
If you use a fuel with an octane rating below the requirement of the engine, 
the management system may move the engine settings into an area of less 
efficient combustion, resulting in reduced power and reduced fuel economy.
You will be losing both money and driveability. If you use a fuel with an 
octane rating higher than what the engine can use, you are just wasting 
money by paying for octane that you can not utilise. The additive packages 
are matched to the engines using the fuel, for example intake valve deposit 
control additive concentrations may be increased in the premium octane grade.
If your vehicle does not have a knock sensor, then using a fuel with an 
octane rating significantly below the octane requirement of the engine means 
that the little men with hammers will gleefully pummel your engine to pieces. 

You should initially be guided by the vehicle manufacturer's recommendations, 
however you can experiment, as the variations in vehicle tolerances can 
mean that Octane Number Requirement for a given vehicle model can range 
over 6 Octane Numbers. Caution should be used, and remember to compensate 
if the conditions change, such as carrying more people or driving in 
different ambient conditions. You can often reduce the octane of the fuel 
you use in winter because the temperature decrease and possible humidity 
changes may significantly reduce the octane requirement of the engine.

Use the octane that provides cost-effective driveability and performance, 
using anything more is waste of money, and anything less could result in
an unscheduled, expensive visit to your mechanic.

6.17 Can I tune the engine to use another octane fuel?

In general, modern engine management systems will compensate for fuel octane, 
and once you have satisfied the optimum octane requirement, you are at the
optimum overall performance area of the engine map. Tuning changes to obtain 
more power will probably adversely affect both fuel economy and emissions. 
Unless you have access to good diagnostic equipment that can ensure 
regulatory limits are complied with, it is likely that adjustments may be 
regarded as illegal tampering by your local regulation enforcers. If you are 
skilled, you will be able to legally wring slightly more performance from 
your engine by using a dynamometer in conjunction with engine and exhaust gas
analyzers and a well-designed, retrofitted, performance engine management 

6.18 How can I increase the fuel octane?

Not simply, you can purchase additives, however these are not cost-effective
and a survey in 1989 showed the cost of increasing the octane rating of one
US gallon by one unit ranged from 10 cents ( methanol ), 50 cents (MMT), 
$1.00 ( TEL ), to $3.25 ( xylenes ) [108]. Refer to section 6.20 for a 
discussion on naphthalene ( mothballs ). It is preferable to purchase a 
higher octane fuel such as racing fuel, aviation gasolines, or methanol. 
Sadly, the price of chemical grade methanol has almost doubled during 1994. 
If you plan to use alcohol blends, ensure your fuel handling system is 
compatible, and that you only use dry gasoline by filling up early in the 
morning when the storage tanks are cool. Also ensure that the service station
storage tank has not been refilled recently. Retailers are supposed to wait 
several hours before bringing a refilled tank online, to allow suspended 
undissolved water to settle out, but they do not always wait the full period. 

6.19 Are aviation gasoline octane numbers comparable?

Aviation gasolines were all highly leaded and graded using two numbers, with 
common grades being 80/87, 100/130, and 115/145 [109,110]. The first number is 
the Aviation rating ( aka Lean Mixture rating ), and the second number is the 
Supercharge rating ( aka Rich Mixture rating ). In the 1970s a new grade,
100LL ( low lead = 0.53mlTEL/L instead of 1.06mlTEL/L) was introduced to 
replace the 80/87 and 100/130. Soon after the introduction, there was a 
spate of plug fouling, and high cylinder head temperatures resulting in 
cracked cylinder heads [110]. The old 80/87 grade was reintroduced on a 
limited scale.  The Aviation Rating is determined using the automotive Motor 
Octane test procedure, and then converted to an Aviation Number using a 
table in the method. Aviation Numbers below 100 are Octane numbers, while 
numbers above 100 are Performance numbers. There is usually only 1 - 2 
Octane units different to the Motor value up to 100, but Performance numbers
varies significantly above that eg 110 MON = 128 Performance number.

The second Avgas number is the Rich Mixture method Performance Number ( PN 
- they are not commonly called octane numbers when they are above 100 ), and 
is determined on a supercharged version of the CFR engine which has a fixed 
compression ratio. The method determines the dependence of the highest 
permissible power ( in terms of indicated mean effective pressure ) on 
mixture strength and boost for a specific light knocking setting. The 
Performance Number indicates the maximum knock-free power obtainable from a 
fuel compared to iso-octane = 100. Thus, a PN = 150 indicates that an engine
designed to utilise the fuel can obtain 150% of the knock-limited power of 
iso-octane at the same mixture ratio. This is an arbitrary scale based on 
iso-octane + varying amounts of TEL, derived from a survey of engines 
performed decades ago. Aviation gasoline PNs are rated using variations of 
mixture strength to obtain the maximum knock-limited power in a supercharged
engine. This can be extended to provide mixture response curves which define
the maximum boost ( rich - about 11:1 stoichiometry ) and minimum boost 
( weak about 16:1 stoichiometry ) before knock [110].

The 115/145 grade is being phased out, but even the 100LL has more octane 
than any automotive gasoline. 

6.20 Can mothballs increase octane? 

The legend of mothballs as an octane enhancer arose well before WWII when
naphthalene was used as the active ingredient. Today, the majority of 
mothballs use para-dichlorobenzene in place of naphthalene, so choose 
carefully if you wish to experiment :-). There have been some concerns about 
the toxicity of para-dichlorobenzene, and naphthalene mothballs have again
become popular. In the 1920s, typical gasoline octane ratings were 40-60 
[11], and during the 1930s and 40s, the ratings increased by approximately 20 
units as alkyl leads and improved refining processes became widespread [12]. 

Naphthalene has a blending motor octane number of 90 [52], so the addition of 
a significant amount of mothballs could increase the octane, and they were 
soluble in gasoline. The amount usually required to appreciably increase the 
octane also had some adverse effects. The most obvious was due to the high 
melting point ( 80C ), when the fuel evaporated the naphthalene would 
precipitate out, blocking jets and filters. With modern gasolines, 
naphthalene is more likely to reduce the octane rating, and the amount 
required for low octane fuels will also create operational and emissions 

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