1. CHRISTIAN PETERSON JOSHUA BIANCO Ignition Optimization

2. Four Stroke Engine Most commonly engine used today Four Stroke Cycle  Intake  Compression  Power  Exhaust Animation (2) Animation Piston makes two complete passes in cylinder to complete one operating cycle (4) (5)

3. 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)

4. 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).)

5. 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

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

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

8. Force a = cos(stroke/rod length) a = cos(84mm/153mm) a = 0.853 [At maximum] F = Area * Pressure Area = pi(r)^2 = 3.14(1.65in)^2 = 8.55 Pressure = 238PSI [Pressure found in Honda F20c FSM]

9. 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

10. Neural Network Training data unavailable.

11. Algorithm For Static Torque Output Varying theta from 0  Π Calculate 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]

12. 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

13. Torque Output Torque ft/lbs Degrees Max Torque found at 17deg BTDC (157.8 ft/lbs)

14. Dynamic Algorithm Based on Piston speed calculate degrees when piston is.34ms before BTDC Input RPM and angle from previous result For each radian only half crank radius vary velocity Calculate velocity of piston = math.sin(radians)*(rpm*.8959) Calculate dist_TDC = math.sin(t)*6.02 Calculate distance moved at velocity = distTDC - deltaDistTDC Return angle BTDC =(180 – result)

15. Ignition Advance at Given RPM Seconds RPM 1000-9000

16. 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.

17. 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)

18. 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.

19. Questions For Us

20. 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%20Engi nes.htm (5) http://www.oceansidemotorsports.com/oceanside-bmw-engine-repair/http://www.oceansidemotorsports.com/oceanside-bmw-engine-repair/ (6) http://www.ajol.info/index.php/ijest/article/view/101720 http://www.ajol.info/index.php/ijest/article/view/101720 (7) https://en.wikipedia.org/wiki/Piston_motion_equations#Crankshaft_geometry