Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
THE AERODYNAMICS OF THE KNUCKLEBALL PITCH: AN EXPERIMENTAL INVESTIGATION INTO THE EFFECTS THAT THE SEAM AND SLOW ROTATION ...
Different Pitches<br />*All of these conditions are dependent upon the individual pitcher.<br />[1] Adair, R.K., The Physi...
Baseball Terminology<br />Four-Seam Orientation<br />Two-Seam Orientation<br />3<br />
Baseball Terminology<br />2 elongated figure “8” pieces of cowhide<br />Cowhide is held together with red stitches<br />Ho...
Background of the Knuckleball<br />Invented by Eddie “Knuckles” Cicotte around 1908<br />Perplexing because path of knuckl...
Background of the Knuckleball<br />Prolific Knuckleball pitchers:<br />Hoyt Wilhelm (5 time All-Star, Hall of Fame)<br />P...
Interview with R.A. Dickey<br />7<br />Jim Caple (ESPN) interview of R.A. Dickey on Mar 17, 2008<br />
Strong Points in Interview with R.A. Dickey<br />Feel is important<br />Places fingernails into horseshoe area for grip<br...
Characteristics of the Knuckleball<br />65 – 80 mph (95 – 117 ft/s)<br />Reynolds number of 1.4x105 to 1.8x105<br />Data w...
Movement of the Knuckleball<br />10<br />ViewDo: How To Throw a Knuckleball. June 16, 2006<br />
Literature Review<br />1672- Newton noticed how flight of tennis ball was affected by spin[3]<br />1852- Magnus found that...
Literature Review<br />1959- Lyman Briggs was first find deflection of baseball due to spin<br />1971- Brown recorded flow...
Literature Review<br />1975- Watts and Sawyer recorded lateral force of baseball in 4-seam orientation at 46 mph as a func...
Motivation and Methodology<br />To find why the knuckleball moves erratically<br />What effect do the seams and rotation h...
Force Balance: Goals<br />Match Watts and Sawyer’s lift data<br />4-seam orientation, 46 mph, statically<br />4-seam orien...
Force Balance: Match Watts and Sawyer’s Data<br />4-Seam baseball, rotating statically, at 46 mph<br />Follow minima and m...
Force Balance: 4-Seam at 46 mph Data<br />Lift oscillates between -0.1 to 0.1 lbs<br />Lift goes in the direction of the n...
Force Balance: Wind Tunnel Setup<br />Force Balance with spinning strut<br />12 V DC motor was used to rotate baseball<br ...
Force Balance: Spinning Strut, Static and Spinning Data<br />Spinning strut data matches previous data<br />19<br />
Force Balance: Frequency Filter<br />20<br />Blade Pass Frequency: 280 Hz<br />
Force Balance: 2-Seam Knuckleball<br />Peak of lift is at 170°<br />Minimum of lift is at 190°<br />Orientation of basebal...
Force Balance: 2-Seam Knuckleball<br />Maximum of lift is at 170°, which is near seam<br />What effect does the seam have ...
Force Balance: Standard Deviations<br />Standard deviation of each lift was found<br />2-Seam, spinning baseball had great...
Flow Visualization: Goals<br />Match existing data<br />Separation on smooth sphere<br />Study how separation changes as b...
Flow Visualization: Setup<br />Sage Action Helium Bubble Generator<br />Photron Fastcam-APX RS CMOS high speed camera<br /...
Flow Visualization: Matlab Code<br />Problem with helium bubbles is that only a few are visible at a given time<br />Matla...
Flow Visualization: Separation on Smooth Sphere<br />Superimposed image of helium bubbles on smooth sphere<br />Separation...
Flow Visualization: Separation on Baseball<br />Seam induces separation<br />Separation on landing strip is at 104±5°<br /...
Flow Visualization: Separation as Baseball Rotates<br />29<br />
Flow Visualization: Details of Separation on Rotating Baseball<br />Separation varies from 88° to 122° during one rotation...
Flow Visualization: Separation and Lift<br />Slight correlation between lift and separation<br />Largest change in separat...
Hot Film Anemometry: Goals<br />Build hot film plug<br />Calibrate with a smooth sphere<br />Match published data<br />Mak...
Hot Film Anemometry: Assembly<br />¼” diameter plug, 1” long<br />Acrylic<br />Aluminum tube<br />5 micron diameter tungst...
Hot Film Anemometry: Calibration<br />Achenbach shear profile was used to calibrate the hot films<br />Achenbach found she...
Hot Film Anemometry: Match Achenbach’s Data<br />Hot film was placed in smooth sphere at same Re of Achenbach, Re=1.6x105<...
Hot Film Anemometry: Shear Stress on a Smooth Sphere with Trip Wire<br />Shear stress was found on smooth sphere with trip...
Hot Film Anemometry: Effect of Trip Wire on Smooth Sphere<br />Tripping wire was placed 60° upstream from the hot film<br ...
Hot Film Anemometry: Positions in Baseball<br />Hot films were placed in the landing strip and between the seams<br />Perp...
Hot Film Anemometry: Morrissey and Achenbach Data<br />Shear stress on landing strip of baseball almost identical to the s...
Hot Film Anemometry: Shear Stress at Landing Strip<br />Stagnation is at 180°<br />Shear stress is zero because flow follo...
Hot Film Anemometry: Shear Stress on Landing Strip<br />Shear stress is greater as the ball rotates away from stagnation<b...
Hot Film Anemometry: Separation Difference in Respect to Rotation <br />Separation is delayed when hot film is rotating aw...
Hot Film Anemometry: Smooth Sphere Trip Wire Compared to Baseball Data<br />Baseball data is when hot film is rotating tow...
Hot Film Anemometry: Delayed Separation and Lift<br />Most knuckleball pitchers hold the baseball at 120° azimuthal angle<...
Hot Film Anemometry: Delayed Separation and Lift<br />At 170°, lift is at it’s maximum<br />A seam is 20° and 40° away fro...
Overall Summary<br />Landing Strip acts as a smooth sphere<br />Flow visualization and hot film<br />Seams carry separatio...
Future Work<br />Lift and lateral forces as function of pressure and humidity<br />Chase Field, Phoenix, Arizona- Lowest h...
Acknowledgements<br />Advisor: Dr. John Borg<br />Committee Members:<br />Dr. Jon Koch<br />Dr. Phillip Voglewede<br />Mac...
Questions?<br />49<br />
BACKUP SLIDES<br />50<br />
Baseball Setup<br />Holes for baseball were found for each orientation<br />4-seam:<br />Midpoint between seams<br />2-sea...
Baseball Orientation<br />Before any setup was constructed, it was important to configure the direction of the force vecto...
Force Balance: Wind Tunnel Setup<br />Design of a peep hole, mirror, and protractor was used to view orientation of baseba...
Force Balance: Calibration<br />Calibration was done with a series of weights<br />Drawing of lift calibration<br />54<br />
Force Balance: Apparatus<br />Force balance recorded lift and drag<br />Force balance was rotated to record lift and later...
Hot Film Anemometry:<br />Data is mirrored at 180°<br />56<br />
Hot Film Anemometry:<br />57<br />
Literature Review<br />2001- Leroy Alaways and Mont Hubbard, along with Sikorsky and Watts and Ferrer’s data found that or...
Force Balance: Magnus Effect<br />Coefficient of Lift, Spin Parameter, is 0.001014<br />59<br />Magnus force is calculated...
Conclusion: Hot Film Anemometry<br />High shear stress when ball is initially rotating<br />Shear stress causes the baseba...
Conclusion: Flow Visualization<br />Seams control rotation rate until the pressure recovers over the seam<br />61<br />
Upcoming SlideShare
Loading in …5
×

Aerodynamics Of A Knuckleball Pitch Presentation

4,131 views

Published on

My Masters thesis defense presentation.

  • Be the first to comment

Aerodynamics Of A Knuckleball Pitch Presentation

  1. 1. THE AERODYNAMICS OF THE KNUCKLEBALL PITCH: AN EXPERIMENTAL INVESTIGATION INTO THE EFFECTS THAT THE SEAM AND SLOW ROTATION HAVE ON A BASEBALL<br />By: Michael Morrissey<br />Advisor: Dr. John Borg<br />Committee Members: Dr. Jon Koch and Dr. Phillip Voglewede<br />
  2. 2. Different Pitches<br />*All of these conditions are dependent upon the individual pitcher.<br />[1] Adair, R.K., The Physics of Baseball. 1994, New York: HarperCollins.<br />2<br />
  3. 3. Baseball Terminology<br />Four-Seam Orientation<br />Two-Seam Orientation<br />3<br />
  4. 4. Baseball Terminology<br />2 elongated figure “8” pieces of cowhide<br />Cowhide is held together with red stitches<br />Horseshoe lies behind seam<br />Landing strip is along long piece of cowhide<br />4<br />
  5. 5. Background of the Knuckleball<br />Invented by Eddie “Knuckles” Cicotte around 1908<br />Perplexing because path of knuckleball never seems to repeat under same conditions<br />“I always thought the knuckleball was the easiest pitch to catch. Wait&apos;ll it stops rolling, then go to the backstop and pick it up.”- Bob Uecker<br />[2] Clark, D., The Knucklebook. 2006, Chicago: Ivan R. Dee.<br />5<br />
  6. 6. Background of the Knuckleball<br />Prolific Knuckleball pitchers:<br />Hoyt Wilhelm (5 time All-Star, Hall of Fame)<br />Phil Niekro (5 time All-Star, Hall of Fame)<br />Jesse Haines (Hall of Fame)<br />Current MLB Knuckleballers:<br />Tim Wakefield, Boston Red Sox<br />R.A. Dickey, Minnesota Twins<br />Josh Banks, San Diego Padres<br />Charlie Haegar, Los Angeles Dodgers<br />6<br />
  7. 7. Interview with R.A. Dickey<br />7<br />Jim Caple (ESPN) interview of R.A. Dickey on Mar 17, 2008<br />
  8. 8. Strong Points in Interview with R.A. Dickey<br />Feel is important<br />Places fingernails into horseshoe area for grip<br />Create late movement<br />“Ball grips into air”<br />Easiest pitch to throw, hardest to master<br />Same pitch, different paths<br />Good places for knuckleball:<br />High wind and humidity<br />Boston and Pittsburgh<br />Bad places for knuckleball:<br />High heat<br />Arizona and Colorado Springs<br />8<br />
  9. 9. Characteristics of the Knuckleball<br />65 – 80 mph (95 – 117 ft/s)<br />Reynolds number of 1.4x105 to 1.8x105<br />Data will be collected at 70 mph<br />Two-seam orientation<br />Rotation rate of 50 rpm<br />One half of a rotation from pitcher to catcher<br />9<br />Tim Wakefield<br />Phil Niekro<br />Eddie Cocotte<br />
  10. 10. Movement of the Knuckleball<br />10<br />ViewDo: How To Throw a Knuckleball. June 16, 2006<br />
  11. 11. Literature Review<br />1672- Newton noticed how flight of tennis ball was affected by spin[3]<br />1852- Magnus found that rotation of cylinder created a lateral force[4]<br />1904- Prandtl discovered the boundary layer concept[5]<br />[3] Newton, I., New Theory of Light and Colours. Philos. Trans. R. Soc., 1672: p. 678-688.<br />[4] Magnus, G., On the Deviation of Projectiles; and on a Remarkable Phenomenon of Rotating Bodies. Memoirs of the Royal Academy, 1852: p. 210-231.<br />[5] Prandtl, L., Essentials of Fluid Dynamics. 1952, New York: Hafner Publishing Company, Inc.<br />11<br />
  12. 12. Literature Review<br />1959- Lyman Briggs was first find deflection of baseball due to spin<br />1971- Brown recorded flow visualization photos of baseball<br />Brown’s photo of a spinning baseball with a rate of 900 rpm, counter-clockwise, and a speed of 70 ft/sec (47 mph). Seams and rotation provide a downward trajectory. (Brown, 1971)<br />Brown’s photo of a stationary baseball. Seams, alone, produce lift. (Brown, 1971)<br />[6] Brown, F.N.M., See the Wind Blow. 1971, Department of Aerospace and Mechanical Engineering, University of Notre Dame.<br />12<br />
  13. 13. Literature Review<br />1975- Watts and Sawyer recorded lateral force of baseball in 4-seam orientation at 46 mph as a function of different azimuthal angle<br />Watts and Sawyer’s orientation of the baseball in the wind tunnel. (Watts and Sawyer, 1975)<br />Watts and Sawyer’s results of the lateral force imbalance of a four-seam baseball as the angle changes. (Watts and Sawyer, 1975)<br />[7] Watts, R.G. and E. Sawyer, Aerodynamics of a Knuckleball. American Journal of Physics, 1975. 43: p. 960-963.<br />13<br />
  14. 14. Motivation and Methodology<br />To find why the knuckleball moves erratically<br />What effect do the seams and rotation have on the aerodynamics of the knuckleball<br />Methods:<br />Force Balance Dynamometry<br />Flow Visualization<br />Hot Film Anemometry<br />14<br />
  15. 15. Force Balance: Goals<br />Match Watts and Sawyer’s lift data<br />4-seam orientation, 46 mph, statically<br />4-seam orientation, 46 mph, spinning<br />Find lift from knuckleball conditions<br />2-seam orientation, 70 mph, spinning<br />15<br />
  16. 16. Force Balance: Match Watts and Sawyer’s Data<br />4-Seam baseball, rotating statically, at 46 mph<br />Follow minima and maxima as well as trend<br />4-seam baseball is symmetric twice<br />16<br />
  17. 17. Force Balance: 4-Seam at 46 mph Data<br />Lift oscillates between -0.1 to 0.1 lbs<br />Lift goes in the direction of the nearest seam<br />There is a variance when the stagnation is at a seam or midpoint between seams<br />17<br />
  18. 18. Force Balance: Wind Tunnel Setup<br />Force Balance with spinning strut<br />12 V DC motor was used to rotate baseball<br />Laser diode system was built to measure rotation rate<br />1 slit chopper plate<br />36 slit chopper plate<br />18<br />DC Motor<br />Photo Diode<br />Laser<br />
  19. 19. Force Balance: Spinning Strut, Static and Spinning Data<br />Spinning strut data matches previous data<br />19<br />
  20. 20. Force Balance: Frequency Filter<br />20<br />Blade Pass Frequency: 280 Hz<br />
  21. 21. Force Balance: 2-Seam Knuckleball<br />Peak of lift is at 170°<br />Minimum of lift is at 190°<br />Orientation of baseball during data collection shown at right<br />21<br />
  22. 22. Force Balance: 2-Seam Knuckleball<br />Maximum of lift is at 170°, which is near seam<br />What effect does the seam have on the lift?<br />Lift goes in the direction of the nearest seam when within 30° from stagnation<br />Lateral force changes positive and negative, but not as much as the lift<br />22<br />
  23. 23. Force Balance: Standard Deviations<br />Standard deviation of each lift was found<br />2-Seam, spinning baseball had greatest variation<br />This concludes that the lift is not consistent per angle of rotation<br />Leads to unpredictability of baseball<br />23<br />
  24. 24. Flow Visualization: Goals<br />Match existing data<br />Separation on smooth sphere<br />Study how separation changes as baseball rotates<br />Find separation on landing strip and across the seams<br />24<br />
  25. 25. Flow Visualization: Setup<br />Sage Action Helium Bubble Generator<br />Photron Fastcam-APX RS CMOS high speed camera<br />Laser diode system<br />HP Oscilloscope<br />Lighting system<br />Two halogen lamps<br />Two fresnel lenses<br />Two black covers<br />Matlab programs<br />25<br />
  26. 26. Flow Visualization: Matlab Code<br />Problem with helium bubbles is that only a few are visible at a given time<br />Matlab code superimposed images together<br />300 helium bubble photographs<br />Protractor<br />Fiducial tracer<br />Matlab code rotated image so stagnation was at 0°<br />26<br />
  27. 27. Flow Visualization: Separation on Smooth Sphere<br />Superimposed image of helium bubbles on smooth sphere<br />Separation is at 107±5°<br />Accepted value is 110°[9]<br />Flow visualization method is correct to use for data collection<br />27<br />[8] Chang, P.K., Separation of Flow. 1970, Oxford, New York: Pergamon Press.<br />
  28. 28. Flow Visualization: Separation on Baseball<br />Seam induces separation<br />Separation on landing strip is at 104±5°<br />Near sphere of 107±5°<br />28<br />
  29. 29. Flow Visualization: Separation as Baseball Rotates<br />29<br />
  30. 30. Flow Visualization: Details of Separation on Rotating Baseball<br />Separation varies from 88° to 122° during one rotation<br />Seam carries separation so separation is induced by the seam<br />Most movement of separation is during first 180°<br />30<br />
  31. 31. Flow Visualization: Separation and Lift<br />Slight correlation between lift and separation<br />Largest change in separation is between 90° to 130°<br />31<br />
  32. 32. Hot Film Anemometry: Goals<br />Build hot film plug<br />Calibrate with a smooth sphere<br />Match published data<br />Make observations with smooth sphere and trip wire<br />Collect data:<br />Landing Strip<br />Before and after seam, clockwise<br />Before and after seam, counter-clockwise<br />32<br />
  33. 33. Hot Film Anemometry: Assembly<br />¼” diameter plug, 1” long<br />Acrylic<br />Aluminum tube<br />5 micron diameter tungsten wire<br />33<br />5 µm tungsten wire<br />
  34. 34. Hot Film Anemometry: Calibration<br />Achenbach shear profile was used to calibrate the hot films<br />Achenbach found shear stress on a smooth sphere as a function of degrees<br />King’s Law was used for shear stress, where n=1/3<br />34<br />[9] Achenbach, E., Experiments on the Flow Past Spheres at Very High Reynolds Numbers. Journal of Fluid Mechanics, 1972. 54: p. 565-575.<br />
  35. 35. Hot Film Anemometry: Match Achenbach’s Data<br />Hot film was placed in smooth sphere at same Re of Achenbach, Re=1.6x105<br />Smooth sphere data fits published data<br />Hot film was placed orthogonal and parallel to the flow<br />Shear stress is much lower when hot film is parallel<br />35<br />[10] Achenbach, E., Experiments on the Flow Past Spheres at Very High Reynolds Numbers. Journal of Fluid Mechanics, 1972. 54: p. 565-575.<br />
  36. 36. Hot Film Anemometry: Shear Stress on a Smooth Sphere with Trip Wire<br />Shear stress was found on smooth sphere with trip wire<br />Hot film parallel to flow was small, once again<br />Hot film upstream of trip wire experienced decrease in shear at 60°<br />Hot film downstream of trip wire experienced largest increase in shear at 45°<br />36<br />
  37. 37. Hot Film Anemometry: Effect of Trip Wire on Smooth Sphere<br />Tripping wire was placed 60° upstream from the hot film<br />Shear stress matches smooth sphere data up to 60°<br />Tripping wire delays separation when trip wire is 10° to 60° from stagnation<br />37<br />
  38. 38. Hot Film Anemometry: Positions in Baseball<br />Hot films were placed in the landing strip and between the seams<br />Perpendicular to free stream velocity<br />Hot films surrounding seam were used while ball was rotating clockwise and counter-clockwise<br />Together, this allowed 5 hot films on one ball<br />38<br />
  39. 39. Hot Film Anemometry: Morrissey and Achenbach Data<br />Shear stress on landing strip of baseball almost identical to the shear stress found by Achenbach<br />39<br />
  40. 40. Hot Film Anemometry: Shear Stress at Landing Strip<br />Stagnation is at 180°<br />Shear stress is zero because flow follows curvature of ball<br />Maximum shear is about 60° from stagnation<br />Turbulent wake 288° to 81°<br />Relatively symmetrical over stagnation<br />Flow visualization images match hot film data<br />40<br />
  41. 41. Hot Film Anemometry: Shear Stress on Landing Strip<br />Shear stress is greater as the ball rotates away from stagnation<br />Local Reynolds number is greater as the hot film rotates towards stagnation<br />Could rotation delay separation on bottom half of baseball?<br />41<br />
  42. 42. Hot Film Anemometry: Separation Difference in Respect to Rotation <br />Separation is delayed when hot film is rotating away<br />Hot film between seams record small amounts of shear stress<br />Hot film upstream of seams have less shear than hot film downstream of seam<br />Hot film downstream of seam has small change of slope at 40°<br />42<br />
  43. 43. Hot Film Anemometry: Smooth Sphere Trip Wire Compared to Baseball Data<br />Baseball data is when hot film is rotating towards stagnation<br />Nearly same trends are noticed of shear stress when hot film is placed upstream and downstream of trip wire and baseball seam<br />Therefore, seam acts as a trip wire<br />Seam delays separation?<br />43<br />
  44. 44. Hot Film Anemometry: Delayed Separation and Lift<br />Most knuckleball pitchers hold the baseball at 120° azimuthal angle<br />Most change in lift is during the knuckleball rotation<br />This large change achieves the deception a baseball pitcher is looking for<br />44<br />
  45. 45. Hot Film Anemometry: Delayed Separation and Lift<br />At 170°, lift is at it’s maximum<br />A seam is 20° and 40° away from each side of stagnation<br />Trip wire shows that separation delay is when trip wire is 10° to 60° from stagnation<br />Therefore, delayed separation occurs on right side of ball. Conclusively, lift is to the left <br />Same occurs at 190° when lift is at it’s minimum<br />45<br />
  46. 46. Overall Summary<br />Landing Strip acts as a smooth sphere<br />Flow visualization and hot film<br />Seams carry separation toward and away from stagnation<br />Flow visualization and hot film<br />Seams initiate and delay separation<br />Initiate at when seam is 90° to 120° from stagnation (flow visualization and hot film)<br />Evidence that separation is delayed when seam is 10° to 60° from stagnation (hot film)<br />Evidence that rotation of baseball delays separation (not confirmed)<br />Magnus effect is only 6.579x10-7 lbs<br />46<br />
  47. 47. Future Work<br />Lift and lateral forces as function of pressure and humidity<br />Chase Field, Phoenix, Arizona- Lowest humidity<br />Minute Maid Ballpark, Houston, Texas- Highest humidity<br />Fenway Park, Boston, Massachusetts- Highest pressure<br />Coors Field, Denver, Colorado- Lowest pressure<br />Flow visualization<br />Bottom half of the baseball<br />Side of the baseball<br />Ink dot and solvent <br />Confirm that seam delays separation<br />47<br />
  48. 48. Acknowledgements<br />Advisor: Dr. John Borg<br />Committee Members:<br />Dr. Jon Koch<br />Dr. Phillip Voglewede<br />Machinists:<br />Ray Hamilton<br />Tom Silman<br />Dave Gibas<br />Dr. Robert Nelson at Notre Dame University<br />48<br />
  49. 49. Questions?<br />49<br />
  50. 50. BACKUP SLIDES<br />50<br />
  51. 51. Baseball Setup<br />Holes for baseball were found for each orientation<br />4-seam:<br />Midpoint between seams<br />2-seam: <br />Repeat 4-seam process on each side<br />Midpoint between points was found<br />Checked with distance between seams<br />51<br />
  52. 52. Baseball Orientation<br />Before any setup was constructed, it was important to configure the direction of the force vectors<br />This was then applied to ELD’s force balance dynamometer<br />52<br />
  53. 53. Force Balance: Wind Tunnel Setup<br />Design of a peep hole, mirror, and protractor was used to view orientation of baseball<br />53<br />
  54. 54. Force Balance: Calibration<br />Calibration was done with a series of weights<br />Drawing of lift calibration<br />54<br />
  55. 55. Force Balance: Apparatus<br />Force balance recorded lift and drag<br />Force balance was rotated to record lift and lateral forces<br />Two different stings were used:<br />Static strut<br />Spinning strut<br />55<br />
  56. 56. Hot Film Anemometry:<br />Data is mirrored at 180°<br />56<br />
  57. 57. Hot Film Anemometry:<br />57<br />
  58. 58. Literature Review<br />2001- Leroy Alaways and Mont Hubbard, along with Sikorsky and Watts and Ferrer’s data found that orientation of baseball and spin parameter changes the lift coefficient<br />The combination of all three data sets, showing the relationship between all three. (Alaways and Hubbard, 2001)<br />[8] Alaways, L.W. and M. Hubbard, Experimental Determination of Baseball Spin and Lift. Journal of Sports Sciences, 2001. 19: p. 349-358.<br />58<br />
  59. 59. Force Balance: Magnus Effect<br />Coefficient of Lift, Spin Parameter, is 0.001014<br />59<br />Magnus force is calculated to be 6.579x10-7 lbs, therefore, negligible<br />
  60. 60. Conclusion: Hot Film Anemometry<br />High shear stress when ball is initially rotating<br />Shear stress causes the baseball to rotate backward<br />60<br />
  61. 61. Conclusion: Flow Visualization<br />Seams control rotation rate until the pressure recovers over the seam<br />61<br />

×