 |
 4 GENUINE ZEBRA TELESCOPIC MEDIUM BLACK INK BALL POINT PENS BLUE 1ST CLS SH $7.99 Time Remaining: 25d 16h 45m Buy It Now for only: $7.99 |
 NEW 1 package BIC Cristal Medium Red Ball Point Ballpoint Ink Pens 10 Count Set $1.99 Time Remaining: 2h 22m Buy It Now for only: $2.99 |
 2X 3in1 BALL POINT PEN + MECHANICAL PENCIL GERMANY LEAD $0.96 Time Remaining: 3h 44m |
 New 9pk Zebra F 301 Stainless Steel Ball Point Pen $14.29 Time Remaining: 9d 4h 21m Buy It Now for only: $14.29 |
 6pcs collectible polymer clay ball point pen for children 877 $0.99 Time Remaining: 7h 11m |
 15 Bic Atlantis Ballpoint Retractable Ball Pen Black Ink Medium Point New $6.99 Time Remaining: 23d 11h 34m Buy It Now for only: $6.99 |
 5 Uni Ball Vision Fine Point Pens Black $3.49 Time Remaining: 8h 34m |
 Dr Grip Retractable Ball Point Pen 4 Pack $9.99 Time Remaining: 9h 33m Buy It Now for only: $11.99 |
 Bic Cristal Bold Colors 10 pack assorted color ball point style pens $2.99 Time Remaining: 4d 1h Buy It Now for only: $2.99 |
 Papermate Eagle M red ball point pen missing cap multi language No Reserve $6.01 (17 Bids) Time Remaining: 11h 36m |
 10 GENUINE ZEBRA TELESCOPIC MED BLACK INK BALL POINT PEN 4C REFILL 1ST CLS SH $7.99 Time Remaining: 14d 2h 4m Buy It Now for only: $7.99 |
 Free shipping Crown ballpoint pen Ball Point Pen Office and Study Pen $0.99 Time Remaining: 18h 24m |
 6pcs Can be foldedfgift olding ball pen ball point penGet good evaluation $0.99 Time Remaining: 18h 33m |
 Uni Ball Onyx Stick Micro Point Roller Ball Pens 12ea $5.99 Time Remaining: 4h 38m Buy It Now for only: $5.99 |
 New Open Box 9 PaperMate Flexgrip 10mm Black Ultra Retractable Ball Point Pens $6.99 (1 Bid) Time Remaining: 18h 42m |
 Rosewood Ball Point Pen Pencil Set Wood Gift Box Storage Case Cross Ink Refill $10.95 Time Remaining: 1d 4h 15m Buy It Now for only: $10.95 |
 AUTHENTIC US GOVERNMENT SKILCRAFT 2 Retractable Ball Point Pens $3.50 Time Remaining: 20h 26m Buy It Now for only: $5.50 |
 5 Uni Ball Jetstream SX 210 roller ball pen black ink 10mm bold point $9.99 Time Remaining: 21h 15m |
 3 Waterman Blue Roller Ball Refill Fine Point 54096P NEW on Card $9.95 Time Remaining: 8d 6h 13m Buy It Now for only: $9.95 |
 LOT OF 20 WILDLIFE HAND CRAFTED HAND PAINTED BALL POINT PENS NIP DISPLAY TUB $7.95 Time Remaining: 1d 1h 58m |
 8 Black BOLD Point PILOT G2 Gel Ink Rolling Ball Pens $9.99 Time Remaining: 19d 23h 23m Buy It Now for only: $9.99 |
 Set of 20 Decorative Ball Point Pens Blue Ink NEW Make Great Gifts In Pairs $14.99 Time Remaining: 1d 2h 48m Buy It Now for only: $19.99 |
 2X 3in1 BALL POINT PEN + MECHANICAL PENCIL GERMANY LEAD $0.96 Time Remaining: 1d 3h 44m |
 Zebra F 301 Retractable Ball Point Pen Black Ink Fine 07mm Stainless Steel 9 PK $14.95 Time Remaining: 14d 6h 53m Buy It Now for only: $14.95 |
 Pens Ball Point Pens 12 pens07mm 12set 3color black 3set+ blue3set+red3set $2.00 Time Remaining: 1d 4h 38m |
 BIC Round Stic Grip Fine Point Ball Pen Blue 12 Count $3.75 Time Remaining: 13d 13h 33m Buy It Now for only: $3.75 |
 Orange Duct Tape Rose Ball Point Pen $2.50 Time Remaining: 1d 7h 52m |
 Pilot Easy Touch Pro Retractable Ball Point Pen Blue Ink 10 mm Lot of 3 $7.50 Time Remaining: 1d 18h 3m Buy It Now for only: $8.50 |
 LOT SALE OF 20 NEW BALL POINT PENS Loc109X $5.00 Time Remaining: 29d 16h 21m Buy It Now for only: $5.00 |
 New Cute Creative Fashion Flexible Cartoon Animals Ball Point PenOfficeStudy Pen $0.99 Time Remaining: 1d 18h 15m |
 New Rosewood Ball Point Pen Wood Gift Box Storage Case Cross Refills Black Ink $7.95 Time Remaining: 25d 21h 56m Buy It Now for only: $7.95 |
 NEW Pentel Wow 18 Pack Retractable Black Ball Point Pens + BONUS $10.99 Time Remaining: 1d 21h 43m Buy It Now for only: $12.99 |
 Pentel Wow Retractable Ball point pens 18 count $7.99 Time Remaining: 1d 22h 11m Buy It Now for only: $8.99 |
 12 Uni Ball Deluxe Rollerball Blue Ink Fine Point $23.99 Time Remaining: 22d 4h 14m Buy It Now for only: $23.99 |
 Lot Of 20 Blue Ink Retractable Ball Point Pens With Clips $7.99 Time Remaining: 1d 23h 44m Buy It Now for only: $8.99 |
 2 New 9ct Zebra F301 Stainless Steel Ball Point Pen $27.89 Time Remaining: 26d 5h 23m Buy It Now for only: $27.89 |
 Pilot Precise V7 fine point rolling ball pens 24 pens black blue $9.95 Time Remaining: 2d 34m |
 Black Ball Point Medium Pen 50 Pcs Brand New $3.12 Time Remaining: 2d 56m |
 Sword Blade Knife Ball Point Pen Blue Ink Stationery Writing Supply Boy Kid Gift $1.89 Time Remaining: 27d 18h 39m Buy It Now for only: $1.89 |
 Clicker Elite Ball Point Pen $0.99 Time Remaining: 2d 3h 38m Buy It Now for only: $3.99 |
 Pilot G Tec C Gel Rolling Ball Pens 5 Pack Pouch Ultra Fine Point 35480 $13.75 Time Remaining: 11d 17h 18m Buy It Now for only: $13.75 |
 Clicker Elite Ball Point Pen $0.99 Time Remaining: 2d 3h 41m Buy It Now for only: $3.99 |
 Clicker Elite Ball Point Pen $0.99 Time Remaining: 2d 3h 42m Buy It Now for only: $3.99 |
 6 Bic Steel Black Medium Point Ball Pen Refills $6.99 Time Remaining: 21d 9h 45m Buy It Now for only: $6.99 |
 2X 3in1 BALL POINT PEN + MECHANICAL PENCIL GERMANY LEAD $0.96 Time Remaining: 2d 3h 44m |
 2 Parker Jotter Purple Retractable Ball Point Pens $7.49 Time Remaining: 21d 21h 22m Buy It Now for only: $7.49 |
 3 Cross Solo CrossSolo Roller Ball Point Pens Stylus $14.95 Time Remaining: 2d 5h 11m Buy It Now for only: $19.95 |
 1 Cross Solo CrossSolo Blue Translucent Ball Point Pen $6.95 Time Remaining: 2d 5h 11m Buy It Now for only: $7.86 |
 Bic Z4+ Roller Ball Pens Black Fine Point 07mm 12 Box Z4C11 $12.89 Time Remaining: 8d 3h 4m Buy It Now for only: $12.89 |
 1 Cross Solo CrossSolo Green Translucent Ball Point Pen $6.95 Time Remaining: 2d 5h 11m Buy It Now for only: $7.86 |
 4 Packs Zebra Fine 007mm Ball Point F Refills Black Ink $6.99 Time Remaining: 6d 3h 27m Buy It Now for only: $6.99 |
 1 Cross Solo CrossSolo Red Translucent Ball Point Pen $6.95 Time Remaining: 2d 5h 12m Buy It Now for only: $7.86 |
 DISNEY TINKERBELL PEN SET 5 PCSCOLLECTORINK PENS BALL POINT $0.99 Time Remaining: 2d 10h 43m |
 5pcsblue colour barrel Zebra BA9 07mm fine ball point pen + 5 refill $11.99 Time Remaining: 16d 4h 19m Buy It Now for only: $11.99 |
 Brand New 1 x Cute Toothpaste shaped Ball point Pen Writing $9.88 Time Remaining: 2d 13h 26m |
 6 PCS PILOT P 700 FINE BALL POINT PEN BLACK smoothest $6.99 Time Remaining: 6d 7h 2m Buy It Now for only: $6.99 |
 Vera Bradley Ball Point Pen Caranby $9.99 Time Remaining: 2d 15h 20m |
 Vera Bradley Ball Point Pen Slate Blooms $9.99 Time Remaining: 2d 15h 20m |
 Zebra K 07mm ball point pen only refill black 10pcs $4.50 Time Remaining: 6d 15h 38m Buy It Now for only: $4.50 |
 Vera Bradley Ball Point Pen Pirouette $9.99 Time Remaining: 2d 15h 21m |
 3x Injection Needle Tube Ball Point Pen Blue Writing $1.59 Time Remaining: 6d 10h 10m Buy It Now for only: $1.59 |
 500 Pens Ball point your name or company name or org or message Black ink $149.95 Time Remaining: 2d 19h 55m |
 Morellato Brand New Executive Ball Point Pen Top Quality Gift Box $19.99 Time Remaining: 2d 23h 55m |
 Papermate Apex 16mm Ball Point Pens Black Ink 14 Count $14.35 Time Remaining: 23d 8h 56m Buy It Now for only: $14.35 |
 Morellato Brand New Executive Ball Point Pen Top Quality Gift Box $22.99 Time Remaining: 2d 23h 55m Buy It Now for only: $26.99 |
 uni ball Vision Rollerball Pens Micro Point Black Dozen 20 value $11.99 Time Remaining: 24d 23h 6m Buy It Now for only: $11.99 |
 uni ball Pink Ribbon 207 Retractable Medium Point Gel Pen New set of 3 $3.29 Time Remaining: 3d 2h 37m Buy It Now for only: $6.99 |
 2X 3in1 BALL POINT PEN + MECHANICAL PENCIL GERMANY LEAD $0.96 Time Remaining: 3d 3h 44m |
 3 New 9pk Zebra F301 Stainless Steel Ball Point Pen $41.84 Time Remaining: 8d 21h 34m Buy It Now for only: $41.84 |
 UNI BALL SIGNO 207 GEL PENS BLUE INK MEDIUM POINT7 8 PACK $10.46 (2 Bids) Time Remaining: 3d 5h 1m |
 30 Papermate Expressions Retractable Ball Point Pens $15.49 Time Remaining: 4d 22h 42m Buy It Now for only: $15.49 |
 Set of two Cross ball point pens 14k gold and Century model $29.00 Time Remaining: 3d 5h 42m Buy It Now for only: $32.00 |
 uni ball 207 Retractable Medium Point Gel Pen Blue Ink Set of 3 New $2.89 Time Remaining: 3d 19h 27m Buy It Now for only: $4.96 |
 Box of 12 Violet Fine Point BK90V BK90 V Pentel RSVP Ball Point Pens $10.99 Time Remaining: 2d 19h 17m Buy It Now for only: $10.99 |
 4 pk uni ball Vision Elite Liquid Rollerball Pens 08 mm Bold Point Black $6.99 Time Remaining: 3d 21h |
 6 Pks PILOT G2 FINE POINT ROLLING BALL RETRACTABLE GEL PENS 31033 LOT 18 NEW $12.95 Time Remaining: 24d 22h 45m Buy It Now for only: $12.95 |
 FISHER SPR4 Space Pen Ball Point Refill Black Medium Point $0.99 (1 Bid) Time Remaining: 3d 23h 17m |
 Pentel Wow Medium Black Retractable Ball Point Pens 3 Packs 12 Pens $4.00 Time Remaining: 3d 23h 57m Buy It Now for only: $4.50 |
 PILOT BP S 07mm fine ball point pen BLACK 12 pcs $7.00 Time Remaining: 24d 4h 55m Buy It Now for only: $7.00 |
 Pentel Wow Medium Black Retractable Ball Point Pens 3 Packs 12 Pens $4.00 Time Remaining: 4d Buy It Now for only: $4.50 |
 6 Parker Ball Point Pen Refill Blue Ink Medium Point $14.99 Time Remaining: 17d 20h 36m Buy It Now for only: $14.99 |
 5pk Pentel RSVP Fine Ball Point Pens Assorted Ink BK90BP5M $0.99 Time Remaining: 4d 9m Buy It Now for only: $3.50 |
 Laser Pointer 4 in 1 Projects 450 feet w LED light Ball point pen PDA stylus $11.99 Time Remaining: 4d 51m Buy It Now for only: $21.99 |
 Avery E Grip Ball Point Pen Black Ink Med Point 12 pack $18.99 Time Remaining: 11d 20h 23m Buy It Now for only: $18.99 |
 2X 3in1 BALL POINT PEN + MECHANICAL PENCIL GERMANY LEAD $0.96 Time Remaining: 4d 3h 44m |
 PILOT BP S 07mm fine ball point pen PURPLE 12 pcs $7.00 Time Remaining: 27d 4h 37m Buy It Now for only: $7.00 |
 Brand New Uni Ball Vision Elite Stick Bold Point Rollerball Pens Assorted Colors $12.99 Time Remaining: 4d 5h 40m Buy It Now for only: $14.99 |
 12 BIC Velocity Ball Point Pen Fine 07mm Retractable Blue New $9.35 Time Remaining: 4d 7h 35m |
 3x Smiling Face Shape Pill Ball Point Pen Cute Lady Favor Telescopic Stationery $1.25 Time Remaining: 29d 13h 57m Buy It Now for only: $1.25 |
 PENTEL RSVP Black Fine Ball Point Pens 5 ct EnerGel X Roller Gel Ink Color 5pc $8.99 Time Remaining: 4d 9h 7m Buy It Now for only: $9.99 |
 Uni Ball Jetstream Sport RT Ballpoint Retractable Pen Blue Ink Bold Point Doz $20.40 Time Remaining: 25d 19h 46m Buy It Now for only: $20.40 |
 Pentel RSVP Red Ink Fine Ball Point Pen 4 Twin Packs 8 Pens $5.95 Time Remaining: 4d 16h 40m Buy It Now for only: $6.95 |
 Lot of Blue Ball Point Ink Pens Clickable W Comfort Grip Buy 10 Get 10 FREE $5.00 Time Remaining: 4d 18h 34m Buy It Now for only: $6.50 |
 4 In 1 Red Beam Laser Pointer LED Torch Ball Point Pen Stylus With Batteries $7.04 Time Remaining: 6d 21h 50m Buy It Now for only: $7.04 |
 Lot of Blue Ball Point Ink Pens Clickable W Comfort Grip Buy 10 Get 10 FREE $5.00 Time Remaining: 4d 18h 35m Buy It Now for only: $6.50 |
 BIC Orange Fine 07mm NEW easy glide ball point pens 12PCS 3 COLOR MIX $7.99 Time Remaining: 14d 19m Buy It Now for only: $7.99 |
 Lot of Blue Ball Point Ink Pens Clickable W Comfort Grip Buy 10 Get 10 FREE $5.00 Time Remaining: 4d 18h 35m Buy It Now for only: $6.50 |
 Lot of Blue Ball Point Ink Pens Clickable W Comfort Grip Buy 10 Get 10 FREE $5.00 Time Remaining: 4d 18h 36m Buy It Now for only: $6.50 |
 Vera Bradley Ball Point Pen LOVES ME New in Box Blue Ink $19.99 Time Remaining: 25d 6h 41m Buy It Now for only: $19.99 |
 96 Retractable Ball point pens Cushion Grip blue New $27.00 Time Remaining: 4d 22h 15m Buy It Now for only: $34.00 |
Point Ball
Golf Ball Dimples & Drag
Golf Ball Dimples & Drag
While few among us can deny that golf is one of the least exciting of all spectator sports, we aerospace engineers are fascinated by its aerodynamics! Even the non-golfers of the world are familiar with the shape of a golf ball, like that pictured below, and have probably wondered why its surface is covered with small indentations called dimples.
Before explaining the purpose of dimples, we first need to understand the aerodynamic properties of a sphere. Let us start by looking at a smooth sphere without any dimples, like a ping-pong ball. If we lived in an ideal world without any friction, the air flowing around a smooth sphere would behave like that shown in the following diagram. In this figure, the angle θ represents position along the surface of the sphere. The leading edge of the sphere that first encounters the incoming airflow is at θ=0° while the trailing edge is at θ=180°. A position of θ=90° is the top of the sphere, θ=270° is the bottom, and θ=360° brings us back around to the leading edge. Note that in this ideal situation, the air flowing around the sphere forms a perfectly symmetrical pattern. The streamline pattern around the front face, from 270° up to 90°, is the same as that around the back face, from 90° down to 270°.
The lower half of this figure also displays the pressure distribution around the surface of the sphere, as represented by the non-dimensional pressure coefficient Cp. Positive (+) values of Cp indicate high pressure while negative (-) values indicate low pressure. It is the differences between high-pressure regions and low-pressure regions that create aerodynamic forces on a body, like lift and drag.
However, this ideal flow pattern tells us something very interesting. Notice that the pressure at the front of the sphere, or θ=0°, is very high. This high pressure indicates that the incoming air impacting against the front face creates a drag force. Nonetheless, the pressure at the back of the sphere, or θ=180°, is also high and identical to that at the front. This high pressure actually creates a thrust, or negative drag, that cancels out the drag on the front of the sphere. In other words, this theoretical situation tells us that there is no drag on a sphere!
Early aerodynamics researchers were quite puzzled by this theoretical result because it contradicted experimental measurements indicating that a sphere does generate drag. The conflict between theory and experiment was one of the great mysteries of the late 19th century that became known as d'Alembert's Paradox, named for famous French mathematician and physicist Jean le Rond d'Alembert (1717-1783) who first discovered the discrepancy.
The reason d'Alembert's ideal theory failed to explain the true aerodynamic behavior of a sphere is that he ignored the influence of friction in his calculations. The actual flowfield around a sphere looks much different than his theory predicts because friction causes a phenomenon known as flow separation. We can better understand this effect by studying the following diagram of the actual flow around a smooth sphere. Here we see that the flowfield around the sphere is no longer symmetrical. Whereas the flow around the ideal sphere continued to follow the surface along the entire rear face, the actual flow no longer does so. When the airflow follows along the surface, we say that the flow is attached. The point at which the flow breaks away from the surface is called the separation point, and the flow downstream of this point is referred to as separated. The region of separated flow is dominated by unsteady, recirculating vortices that create a wake.
The cause of this separation can be seen in the above pressure distribution around the sphere. As the flow moves downstream from the θ=90° or θ=270° position, it encounters an increasing pressure. Whenever a flow encounters increasing pressure, we say that it experiences an adverse pressure gradient. The change in pressure is called adverse because it causes the airflow to slow down and lose momentum. As the pressure continues to increase, the flow continues to slow down until it reaches a speed of zero. It is at this point that the air no longer has any forward momentum, so it separates from the surface.
Once the flow separates from the surface, it no longer results in the ideal pressure distribution shown as the dashed line. Instead, a separated flow creates a region of low pressure in the wake. We see this behavior over the rear face of the sphere from 90° < θ < 270°. Here, the actual pressure distribution, shown as the solid line, remains negative, in contrast to the ideal prediction. The pressure on the front face is still high, however, just as it was for the ideal sphere. Since the pressure is now much higher on the front face than it is on the rear face, the net result is a drag force exerted on the sphere. By accounting for the effect of friction, theory and experiment come into agreement and d'Alembert's Paradox is reconciled.
This explanation leads us to an important conclusion: the drag on a sphere is dominated by the flow separation over its rear face. If we could somehow minimize that separation, the drag experienced by the sphere would be significantly reduced.
Reynolds number (Re) is an important non-dimensional parameter that is used to relate the size of an object to the flow conditions it experiences, and is defined by the equation
Re= ρ V∞ l/ μ
where
ρ = atmospheric density
V∞ = velocity
l = reference length (in the case of a sphere, this variable is defined as the diameter)
μ = viscosity (or friction)
In other words, any two spheres that experience the same Reynolds number should exhibit the same aerodynamic characteristics even if the spheres are of different sizes or flying at different speeds. The above figure indicates that there is a significant change in the drag on a smooth sphere at a Reynolds number of about 3x105. Below this Re, the drag coefficient is roughly constant at 0.5. Above this Re, the drag coefficient again becomes nearly constant at about 0.1.
What is it about this particular Reynolds number that causes such a large reduction in drag? It turns out that it is at this critical point that the air flowing around the sphere makes an important change. We have already discussed the concept of flow separation. One of the key factors affecting flow separation is the behavior of the boundary layer. The boundary layer is a thin layer of air that lies very close to the surface of a body in motion. It is within this layer that the adverse pressure gradient develops that causes the airflow to separate from the surface.
At low Reynolds numbers, the boundary layer remains very smooth and is called laminar. Laminar boundary layers are normally very desirable because they reduce drag on most shapes. Unfortunately, laminar boundary layers are also very fragile and separate from the surface of a body very easily when they encounter an adverse pressure gradient. This separated flow is what causes the drag to remain so high below the critical Reynolds number.
At that Reynolds number, however, the boundary layer switches from being laminar to turbulent. The location at which this change in the boundary layer occurs is called the transition point. A turbulent boundary layer causes mixing of the air near the surface that normally results in higher drag. However, the advantage of turbulence is that it speeds up the airflow and gives it more forward momentum. As a result, the boundary layer resists the adverse pressure gradient much longer before it separates from the surface.
The difference in the flowfields around a smooth sphere and a rough, or dimpled, sphere can be seen above. Since the laminar boundary layer around the smooth sphere separates so rapidly, it creates a very large wake over the entire rear face. This large wake maximizes the region of low pressure and, therefore, results in the maximum difference in pressure between the front and rear faces. As we have seen, this difference creates a large drag like that seen below the transition Reynolds number.
The transition to a turbulent boundary layer, on the other hand, adds energy to the flow allowing it to remain attached to the surface of the sphere further aft. Since separation is delayed, the resulting wake is much narrower. This thin wake reduces the low-pressure region on the rear face and reduces the difference in pressure between the front and back of the sphere. This smaller difference in pressure creates a smaller drag force comparable to that seen above the transition Reynolds number.
These results tell us that causing a turbulent boundary layer to form on the front surface significantly reduces the sphere's drag. For a given sphere diameter, a designer has only two options encourage this transition, either 1) increase the speed of the flow over the sphere to increase the Reynolds number beyond transition or 2) make the surface rough in order to create turbulence. The latter case is often referred to as "tripping" the boundary layer.
In the case of a golf ball, increasing the speed is not an option since a golfer can only swing the club so fast, and this velocity is insufficient to exceed the transition Reynolds number. That leaves tripping the boundary layer as the only realistic alternative to reducing the drag on a golf ball. The purpose of the dimples is to do just that--to create a rough surface that promotes an early transition to a turbulent boundary layer. This turbulence helps the flow remain attached to the surface of the ball and reduces the size of the separated wake so as to reduce the drag it generates in flight. When the drag is reduced, the ball flies farther. Some golf ball manufacturers have even started including dimples with sharp corners rather than circular dimples since research indicates that these polygonal shapes reduce drag even more.
The reason we do not see dimples on other shapes, like wings, is that these particular forms of boundary layer trips only work well on a blunt body like a sphere or a cylinder. The most dominant form of drag on these kinds of shapes is caused by pressure, as we have seen throughout this discussion. More streamlined shapes like the airfoils used on wings are dominated by a different kind of drag called skin friction drag. These streamlined bodies, like that pictured above, have a teardrop shape that creates a much more gradual adverse pressure gradient. This less severe gradient promotes attached flow much further along the body that eliminates flow separation, or at least delays it until very near the trailing edge. The resulting wake is therefore very small and generates very little pressure drag.
However, there do exist other types of devices commonly used on wings that create a similar effect to the dimples used on golf balls. Though these wing devices also create turbulence in order to delay flow separation, the purpose is not to decrease drag but to increase lift. One of the most popular of these devices is the vortex generator.
Vortex generators are often placed along the outer portion of a wing in order to promote a turbulent boundary layer that adds forward momentum to the flow. As in the case of the golf ball, this turbulent boundary layer helps the flow overcome an adverse pressure gradient and remain attached to the surface longer than it would otherwise.
A related device that is most commonly used on high performance fighters is the leadingedge extention(LEX), like that shown above. Both the vortex generator and the LEX are primarily used to delay the flow separation that occurs when operating at high angles of attack near stall. As angle of attack increases, the adverse pressure gradient along the airfoil becomes increasingly stronger. Once the stall angle is reached, the gradient becomes so strong that it forces the flow to separate resulting in a loss of lift or control effectiveness. The advantage of devices like vortex generators and leading edge extensions is that they force the flow to remain attached at higher angles of attack and increase the stall angle. This improvement gives planes likes fighters greater maneuverability while increasing the safety of commercial airliners.
About the Author
What's the best way to get a ball-point pen mark out of khaki colored dress pants?
It's that oil-based ink found in regular Bic ball-point pens I think--not the water-based ink found in some pens. I've washed it with regular detergent a few times and it hasn't come out. Please help. I need these pants to look nice for job interviews. Thanks!
Hairspray works but you need to wet the ink with hairspray and then rub bar soap on it. For big blotches of ink spray wet twice and rub soap on it twice then wash in COLD water. You can do this even if you've tried other ways.
Michael Jordan: 69 points vs Cavs 1990 (career high)