CHRISTIAN PETERSONJOSHUA BIANCO

Ignition Optimization

Four Stroke Engine

Most commonly engine used todayFour Stroke Cycle

Intake Compression Power Exhaust

Animation (2)

Piston makes two complete passes in cylinder to complete one operating cycle (4)

(5)

What is Ignition Timing?

“Measure of time (in degrees of crankshaft rotation) of the point at which a spark plug fires in the compression stroke of each cylinder.” (1)

Measured in degrees before (in advance of) Top Dead Center (BTDC).

Seeks to find the optimal time for spark to occur in the combustion chamber.

(3)

Why is Ignition Timing Important?

Proper ignition timing can cause gasoline to burn more efficiently, reducing wasted energy and lowering emissions.

Proper ignition timing can cause an engine to run cooler by working to improve rotational-momentum instead of fighting against it. This reduces internal stress and friction levels.

By optimizing the ignition timing, we can manipulate and optimize engine power output (by maximizing the area under the curve Torque throughout a given rev-band(1000-9000).)

Informal Statement

We seek to improve the combustion rate of Honda S2000 F20c internal combustion engine by optimizing piston angle with respect to spark-plug ignition, through the use of tests and algorithmic computations. Formula

Max Torque = Summation 1000 9000 (F/cos(α)*sin(ϑ+α)) F = Angular Momentum T = Time NET TQ = ΔL/ΔT = dL/dT InTQ = F*D(sinΘ) Flame speed (F) = 32.8 ft/s <= F <= 82.0 ft/s

Formal Problem Statement

• Force(F) = Area * Pressure• α = sin(θ)*0.853• Θ = λ + (0 -> 3.14)• λ = Starting Position of Piston in Radians

Alpha

a = cos(stroke/rod length)a = cos(84mm/153mm)a = 0.853 [At maximum]

Force

a = cos(stroke/rod length)a = cos(84mm/153mm)a = 0.853 [At maximum]

F = Area * PressureArea = pi(r)^2 = 3.14(1.65in)^2 = 8.55Pressure = 238PSI

[Pressure found in Honda F20c FSM]

Algorithms

Algorithm for calculating torque at a specified RPM for a range of degrees (α) before and after TDC.

[Static Torque Optimization] Algorithm for determining the optimum crankshaft

position, in radians, for a given RPM. FFNN

Neural Network

Training data unavailable.

Algorithm For Static Torque Output

Varying theta from 0 ΠCalculate alpha α=(sin(ϑ+λ)*(α0))

F = Decaying Force = 8.55*(Sin(ϑ)*238)r = RPM( 1000 9000)Complexity of (Torque) = O(n^4) [N refers to the number of iterations from 0-3.14]

Code for Torque Output

def torque_output(lam): alpha = 0.0 theta = 0.0 sum = 0.0 while(theta < 3.14): alpha = math.sin(theta + lam)*(.853) force = decayForce(theta+lam) sum += (force/math.cos(alpha))*(math.sin(theta + alpha)) theta += .01 return sum

def decayForce(theta): return (math.cos(theta/2)*238)*4

Torque Output

Torque ft/lbs

Degrees

Max Torque found at 17deg BTDC (157.8 ft/lbs)

Dynamic Algorithm

Based on Piston speed calculate degrees when piston is .34ms before BTDC

Input RPM and angle from previous resultFor each radian only half crank radius vary

velocityCalculate velocity of piston =

math.sin(radians)*(rpm*.8959)Calculate dist_TDC = math.sin(t)*6.02Calculate distance moved at velocity =

distTDC - deltaDistTDCReturn angle BTDC =(180 – result)

Ignition Advance at Given RPM

Seconds

RPM 1000-9000

Future Work

We will modify code to varying engine models beside the S2000 F20c

Expand algorithms considering more factors like differing octane levels, varying stroke lengths, and changing burn rates.

Why this is relevant to Algorithms Analysis and Design class?

Comparison of multiple algorithms for finding torque output

Designing algorithms to model results of problems found in real world (maximizing torque output)

Questions For Class

How does proper ignition timing effect 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.

What is the complexity for finding ignition timing 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)

Why is a static ignition schedule no longer implemented in modern engines?

As a piston accelerates, ignition needs to accelerate as well.

Questions For Us

Sources

(1) http://arrc.ebscohost.com/ebsco_static/repair-tips/8852.htm#8852CH13_IGNITION_TIMING.htm

(2) http://www.animatedengines.com/otto.html

(3) http://www.waybuilder.net/sweethaven/MechTech/Automotive01/default.asp?unNum=1&lesNum=3&modNum=4

(4) http://courses.washington.edu/engr100/Section_Wei/engine/UofWindsorManual/Four%20Stroke%20Cycle%20Engines.htm

(5) http://www.oceansidemotorsports.com/oceanside-bmw-engine-repair/

(6) http://www.ajol.info/index.php/ijest/article/view/101720

(7) https://en.wikipedia.org/wiki/Piston_motion_equations#Crankshaft_geometry