1
Algorithm Comparisons for Ignition Timing Optimization
Christian Peterson and Joshua Bianco
December 2, 2015
University of North Carolina Wilmington
Abstract
Ignition timing is the process of setting
the angle at which a spark will occur in the
compression cycle of a four-stroke internal
combustion engine with respect to piston
position and crankshaft angular velocity. This
paper discusses the algorithms used to find an
optimal position before top dead center (BTDC)
to maximize toque output of a Honda S2000
F20c stock engine. The first algorithm is based
on a static approach where torque output is
calculated based on a specified engine
revolutions-per-minute (RPM) for varying
degrees alpha and theta before and after top
dead center (TDC)[1]. Alpha is a measure of
degrees from the connecting rod to the line of
motion of the piston, and theta is the angular
position of the crank [5]. The second algorithm
takes a dynamic approach for determining the
optimal crankshaft position given a specific
RPM and producing an angle for optimal
ignition timing. The results of our algorithms
produced similar ignition advance timing for
varying RPM in the range 1000-9000. The
optimal timing advance is between two and
eighteen degrees with a maximum torque output
at seventeen degrees BTDC.
Key Words: ignition timing, static timing,
dynamic timing, ignition optimization
up in the cylinder and will be wasted trying to
push the piston back down before it has reached
the end of its cycle. If the timing is set too late
(too retarded) the pressure from the ignited fuel
air mixture will be lost and will not contribute
the maximum force on the piston moving down
in the power stroke, which will result in a major
loss of torque output [5].
Ignition timing varies greatly based on
the travelling speed of the piston, which is
measured by engine RPM. The higher the RPM
the more ignition advance needed, since the
engine requires more fuel to run at higher speeds
the total combustion process will require more
time to complete. In order to account for the
longer burn time of the fuel mixture the spark
must be advanced in the stroke so that maximum
pressure is achieved just before the pistons
travels down in the cylinder, maximizing the
output of the engine and reducing friction placed
on the crankshaft.
2. Methods
For the static and dynamic algorithms we
are testing on a stock Honda S2000 F20c engine.
The bore of this four-stroke engine measures 87mm
or 3.4252in, the rod length measures 153mm or
6.02362in, and the stroke is 84mm or 3.30709in. The
F20c engine has an output of ~237Hp and 153 ft. lb.
torque and redlines at 9200RPM [2].
1. Introduction
2.1 Static Algorithm
Ignition timing is an important factor in
tuning an internal combustion engine. The
proper timing and spark advance optimize
engine performance by producing more torque
output per cylinder and reducing emissions.
Proper ignition timing results in a cooler engine
by working to improve rotational-momentum of
the crankshaft. If timing is set too early (too
advanced) and the piston is not near TDC the
force will be applied against the piston travelling
The static algorithm is designed to
calculate the maximum torque output at a
specified RPM for a range of degrees
represented by alpha before and after TDC. This
algorithm takes an input lambda, which is
calculated based upon the velocity of the piston
in the engine, the distance travelled by one
piston in the cylinder, and the distance to
cylinder TDC at a specific RPM. The algorithm
2
then calculates the force applied to one piston
during its movement along the rotation of the
crankshaft radius from top where the crankshaft
angle is at 0 degrees and the connecting rod
angle is 180 degrees, or 0 to pi radians, to
bottom where the crankshaft angle is at 180
degrees and connecting rod is at 0 degrees, or pi
to 0 radians. The algorithm only calculates the
force applied in the first half of the crank radius
since the rest of the stroke is used for moving
the piston back to TDC in the cylinder and does
not contribute to the total torque output of the
engines stoke.
The torque output is produced by
calculating the summation of the force applied to
the piston over the ranging theta, or the angular
position of the crankshaft, from 0 to pi radians in
the crank radius where the piston is travelling
down the cylinder [1]. For each iteration or
radian along the crank radius, alpha, the measure
in degrees from the connecting rod to the pistons
line of motion, is calculated by taking the sine of
the sum of the theta value and lambda value at a
given position along the crank radius [5]. The
force is then calculated with each alpha, lambda
and theta value, the force has been decayed since
maximum force should occur at the top of the
stroke pushing the piston downward and
decrease throughout one half the piston cycle
before reaching bottom dead center (BDC) in the
cylinder.
angle and the sine of the sum of the theta and
alpha angles.
F=(F/cos(alpha)*sin(theta + alpha)[1]
The force is decayed by taking the cosine of half
the given theta angle multiplied by nominal
cylinder pressure (238PSI) and then multiplied
by an ignition pressure multiplier of 4.0 [2].
DF=cos(theta/2)*(238)*(4.0)
These calculations are performed for each
iteration along half the crank radius resulting in
the total torque output of the engine.
The complexity of this algorithm in its
worst case is represented by O(n) where n is the
range of degrees before and after TDC tested.
For testing we tried values from -180 to 180
degrees, for each degree tested the torque
function had a function call to calculate a
lambda value O(n+3) with three separate
function calls O(1)*3 to convert from degrees to
radians, calculate piston speed, and calculate
distance moved. For each call to the torque
function we calculated at RPM’s from 10009000 O(9). For the 361 degrees tested there was
a function call to decay force O(1). The final
results were added to a list and iterated through
printing the results O(n).
O(361) + O(9) + O(n+1) +O(n+1) + O(n+1) +
O(1) + O(n)  374+O(3n) = O(n)
2.2 Dynamic Algorithm
The dynamic algorithm is designed to
calculate the angle at which the piston should be
located before TDC when the spark occurs in the
piston for varying engine RPM. Based on a
constant burn rate of .34 milliseconds the
combustion should begin alpha degrees before
TDC and complete as the piston moves
downward with maximum force being exerted at
TDC.
[1]
The total force of a single piston is
calculated by taking the product of the force at a
given radian divided by the cosine of the alpha
The dynamic algorithm takes an input of
engine RPM ranging from (1000-9000) and the
previously calculated angle BTDC to calculate
the degrees BTDC for fuel ignition for the next
RPM in the sequence. For each degree along
half the crank radius the velocity of the piston is
calculated by taking the sine of the product of
3
the radians alpha and the product of the given
RPM and .9859.
PV=sin(alpha)*(RPM*.8959)[3]
Along with each radian around half the crank
radius a range of velocities was tested to
calculate the optimal ignition advance.
After calculating the velocity of the
piston at a given RPM the algorithm calculates
the distance to TDC in the cylinder at that piston
velocity. The distance to TDC is calculated by
taking the result of the product pi minus the
angle theta divided by pi and the engine rod
length (6.02in).
dis_TDC=(pi-theta)/pi*6.02
After calculating the distance to TDC the
algorithm calculates the distance moved at that
velocity and returns the result. The proper
timing angle is represented by (180 degrees –
result). The result from the first iteration is
returned to determine the optimal angle for the
next RPM in the range. The initial angle passed
in for the starting value is 0 degrees or TDC.
The complexity of this algorithm at its
worst case is O(n^n) where n is represented by
the range of degrees before and after TDC
tested. For each varying degree tested there was
a method call to convert degrees to radians,
calculate piston speed and calculate distance
moved O(1). For each degree tested there was a
range of velocities tested O(180^180). For each
RPM 1000-9000 an optimal degree was
determined O(9).
the two algorithms took different strategies to
produce optimal ignition timing advance the
results were very comparable. Below is the
resulting torque output generated by the static
timing algorithm giving a peak torque at 17
degrees BTDC.
The results from the dynamic algorithm show
optimal ignition advance with ranging RPM
from 1000-9000 to be between two and eighteen
degrees BTDC. Which matches the seventeen
degrees advance specified by the static
algorithm for maximum torque output.
O(180^180) = O(9(n^n))  O(n^n)
3. Results
The static algorithm produced the
highest torque output at approximately
seventeen degrees BTDC, the torque recorded at
this timing advance was around 157 ft. lbs. just
over the recorded 153 ft. lbs. stated by the
specification sheet [2]. The dynamic algorithm
produced ignition advance times ranging from 2
to 18 degrees BTDC for RPM’s ranging from
1000-9000. These results are very similar to the
projected timing advance and torque output
found for the Honda S2000 F20c engine. While
4. Future Work
Future improvements to our work will
include making the algorithms customizable for
any four-stroke engine not just the Honda S2000
F20c. Other factors that will be accounted for
will include varying fuel quality (octane), and
stroke lengths along with differing burn rates.
Tuned engines are also a possibility for
improvement including supercharged engines.
5. Questions
4
1. How does proper ignition timing affect torque
output of a four-stroke internal combustion
engine?
 Answer: If the spark occurs too early it
will cause “engine knock” (when the
combustion process occurs too early and
pushes against an ascending piston); if it
occurs too late power will be wasted.
2. What is the complexity for finding ignitiontiming advance using the Static Optimization
algorithm?
 Answer: O(361) + O(9) + O(n+1)
+O(n+1) + O(n+1) + O(1) + O(n)
 374+O(3n) = O(n)
3. Why is a static ignition schedule no longer
implemented in modern engines?
 Answer: As a piston accelerates,
ignition needs to accelerate as well.
6. References
[1] Gupta, B., Rehman, A., & Mittal, N. (2014).
Validating experimentally the gain in torque due
to crankshaft offset of an internal combustion
engine. International Journal of Engineering,
Science, and Technology, 6(2), 76-88. Retrieved
October 14, 2015.
[2] Honda F20C Engine. (n.d.). Retrieved
November 1, 2015, from
http://www.jdmspecengines.com/hondaengines/f-series/f20c.html
[3] L&M Engines, Inc. - Piston Velocity
Calculator. (n.d.). Retrieved September 3, 2015,
from https://www.lmengines.com/piston-speedcalculator/
[4] Derivation of Slider-Crank Model. (n.d.).
Retrieved September 18, 2015, from
http://www.engr.colostate.edu/~allan/thermo/pa
ge2/page2.html
[5] Shiffer, M. (n.d.). Ignition Timing
Explained/Timing an Unknown Engine.
Retrieved October 17, 2015, from
http://www.type2.com/library/electrip/timex.htm
[6] Piston Motion Basics -. (2014, August 8).
Retrieved September 14, 2015, from
http://www.epieng.com/piston_engine_technology/piston_moti
on_basics.htm