Jump to content

Steer for the Rear - Ch13 of TOTWII


Jaybird180

Recommended Posts

I've been thinking about this new chapter (I could almost swear it wasn't in my book before- LoL) and it seems that there's a jewel in there about the bike steering about the rear wheel (once leaned over). And it makes sense to me. But there's a part of me that having a hard time with it and it's the mantra about 40/60 F/R weight distribution and using the throttle properly to arrive at that ratio and NOT exceeding it.

Then that chapter goes on to point out that one could lift the front while leaned over and the bike will continue through the corner. I've seen it done many times (on TV, haven't experienced it myself). So if this is the case, why do we care about 40/60?

Looking through the forum, I came across another thread where I somewhat asked a similar question regarding roll-on rates...which tells me that I've got plenty to understand about the topic of throttle management.

  • Thanks 1
Link to comment
Share on other sites

20 hours ago, Jaybird180 said:

................ Then that chapter goes on to point out that one could lift the front while leaned over and the bike will continue through the corner. I've seen it done many times (on TV, haven't experienced it myself). So if this is the case, why do we care about 40/60?.......

We care the most about inducing the 40/60 weight distribution via throttle control when we need maximum performance from the tires and the suspension, when cornering on asphalt as fast as possible.

If, while cornering like that, we put more weight on one tire, we compress that suspension and load that tire beyond the optimum state or conditions.  The suspension becomes harder, the contact patch becomes a little bigger and the profile of the tire less pliable.  Following the irregularities of the pavement is more difficult for the tire.  The rubber becomes less elastic and it changes its shape more slowly.  Once the weight carried by that tire while cornering hard reaches a crtical point, the available traction that the over-loaded tire can offer rapidly decreases.

During a leaned wheelie, all the weight of the bike and the rider is on the rear tire and on the rear suspension.  That tire would not be able to develop the traction demanded by the lateral forces of extreme cornering, which normally surpass the value of that weight.  The wheelie always happens during the way out of the corner and at a lean angle that is much smaller than the max lean angle required by that turn.  If the rider tries to wheelie the bike at that max lean angle, when the lateral forces of cornering on the contact patch are close to the max, the tire would slide.  The tire would not slide only if the rear contact patch has been unloaded enough from lateral forces in a way that its performance can be reduced by the the extra weight.

  • Like 1
Link to comment
Share on other sites

One the bike is on trajectory, we don't need the front anymore. The rear tire can support the full weight of the rider and bike combination. The power applied extends the suspension and yes the load to the tire increases. Fortunately, friction is directly related to load applied so therefore the load resists the tire sliding.

Assuming we're talking about fresh rubber and not concerned about longevity, why do we care about having 40% of the load on the front. Why not get the power to the ground to the maximum that it translates into forward motion? 

Link to comment
Share on other sites

When you start wheelying some of your power is lifting the front wheel, instead of being translated into forward motion (speed). So if you are interested in lap times, you want all of the power you are requesting with the throttle to go into forward motion when exiting a corner rather than lifting the front wheel. If you are also interested in enjoying yourself you don't mind the wheelies coz they are great fun :) The most obvious demonstration of this wasted power is race starts where a rider who wheelies immediately loses tenths to those who are not. From my own experience, the time lost when doing some wheelies on corner exit is negligible and you can ride it out with the front wheel at a consistent height off the ground until the next gear change, which often puts the front wheel back down. One thing to note is that it's easy to have the front wheel turned when it touches down again if you wheelie while leaned over. There are few things more satisfying than wheelying out of a corner while leaned over, touching down with the front wheel turned slightly, but keeping it pinned, relaxing your arms on the bars and riding it out without having a massive tank slapper. On the dirt bike you can even do this while the rear wheel is spinning and roosting the rider behind you. Especially if that rider is your mate with whom you've been having a roosting war for years :lol:

  • Like 1
Link to comment
Share on other sites

12 hours ago, DucPati said:

When you start wheelying some of your power is lifting the front wheel, instead of being translated into forward motion (speed). So if you are interested in lap times, you want all of the power you are requesting with the throttle to go into forward motion when exiting a corner rather than lifting the front wheel.

This is pure speculation but I'd imagine that the front wheel begins to lift at a point well above 60% weight distribution. But if you could instead find a balance point where all of the power being used it for propulsion than lifting the front wheel, where would that be in relation to the ideal 60%?

  • Thanks 1
Link to comment
Share on other sites

7 hours ago, Jaybird180 said:

This is pure speculation but I'd imagine that the front wheel begins to lift at a point well above 60% weight distribution. But if you could instead find a balance point where all of the power being used it for propulsion than lifting the front wheel, where would that be in relation to the ideal 60%?

Remember that the 60% is not exact, the ideal weight distribution depends on the bike and also the tyres.

I don't know the answer for sure, but logic suggests that if the front wheel is not lifting all the power is going into forward motion (minus power train losses, and anything wasted by rear suspension movement). So even if the front is off the ground, but is not lifting or dropping, all the power is going into forward motion.

My observations while at the track seem to support this - an RSV4 had overtaken me before the chicane going onto the start/finish straight and just after that chicane is a crest which most bikes will wheelie over. I had tucked in behind the RSV4 on my 1098 and he wheelied while I didn't, which allowed me to pull alongside. Not sure whether this was rider skill or wheelie control but the front wheel of the RSV4 then hovered at a consistent height and the RSV4 was able to pull away. Of course it has a lot more power than my 1098 anyway so that's a factor too (he may have been wasting power and still have enough to pull away). But that particular rider is a nutcase so there's that factor too :lol:

  • Like 1
Link to comment
Share on other sites

21 hours ago, Jaybird180 said:

One the bike is on trajectory, we don't need the front anymore. ................why do we care about having 40% of the load on the front. Why not get the power to the ground to the maximum that it translates into forward motion? 

I believe that the answer to your question can be found in the last section of that chapter: Stable suspension.

Perhaps re-reading Chapter 3 could help you see the whole picture more clearly.

  • Thanks 1
Link to comment
Share on other sites

Thanks for the suggestion to re-read some material. I'd come to that same conclusion as I began thinking this through on my way to work this morning. I do need to talk through some things as I read and also some thoughts:

  1. In Ch 2, the section on throttle control, one of the margin comments mentions that it's possible to get on the gas too early and cause the bike to run wide. In light of my new understanding of what the rear does in a corner, in that it's the dissimilar circle size on the side of the rear tire that causes the bike to turn I now ask :does the (greedy) application of throttle really cause a bike to run wide while leaned over? We already have observed that we can lift the front with throttle and the bike will remain as sure as if on rails.
  2. Ch 2 also give the reason for the idea behind the 60/40 and that it's based on a comparative measurement of footprint, nothing more. 0.1-0.2g of throttle is what's needed to maintain that relative contact patch. But since we now understand that size of contact patch isn't the determining factor in available traction should maintenance of footprint still be a Primary concern as requested by Ch2?

I'd like to make a note here: I'm not advancing an idea of "whacking" open the gas, nor am I saying that a smooth roll-on isn't the right thing to do. I am saying that perhaps we needn't be as gentle with the throttle as I previously thought. If this is really the case, then perhaps I opened a door for more available attention for other things. I hope I'm not opening the door to more highsides.

    3. Donny Greene in his comment at the end of Ch 3 says it this way: "Once you have the throttle control rule firmly understood and practiced and you can get the rear wheel spinning with a smooth roll-on, your bike will handle again." What if instead of spinning the rear, you time your roll rate so that the tire is hooked up and driving forward? I can see a viable reason to want to use a spinning rear wheel to help finish the corner, but it might be too much mid-corner even if it does work just fine for Casey Stoner.

Link to comment
Share on other sites

There is a section in Ch 13 called "Front End Duties" that talks about how the front end still contributes, and also addresses getting on the gas too early.

Notice that when it says in TOTWII that the bike will maintain its lean angle even with the front wheel off the ground, it does NOT say that you have maximum corner speed/traction in that situation (you don't), and the section referenced above on front end duties talks about that.

While you do see racers commonly wheelie out of corners, you don't see them wheelie in the middle of the corner at max lean angle, because you just can't load the rear that much at max speed and lean, it would lose traction before it would wheelie.

Another thing to note is that while acceleration alone can and does cause wheelies, another thing that can contribute is the release (rebound) of the front suspension as the bike is coming out of the corner, and that may be some of what you are seeing in racing. Some riders - not going to name any names here -  when launching a big show-off wheelie, use a sharp suspension compression/rebound to help loft the front.

  • Like 1
Link to comment
Share on other sites

1 hour ago, Hotfoot said:

There is a section in Ch 13 called "Front End Duties" that talks about how the front end still contributes, and also addresses getting on the gas too early.

Notice that when it says in TOTWII that the bike will maintain its lean angle even with the front wheel off the ground, it does NOT say that you have maximum corner speed/traction in that situation (you don't), and the section referenced above on front end duties talks about that.

While you do see racers commonly wheelie out of corners, you don't see them wheelie in the middle of the corner at max lean angle, because you just can't load the rear that much at max speed and lean, it would lose traction before it would wheelie.

Another thing to note is that while acceleration alone can and does cause wheelies, another thing that can contribute is the release (rebound) of the front suspension as the bike is coming out of the corner, and that may be some of what you are seeing in racing. Some riders - not going to name any names here -  when launching a big show-off wheelie, use a sharp suspension compression/rebound to help loft the front.

MM93 has been seen doing this as well as Aaron Yates.

Link to comment
Share on other sites

On 12/15/2017 at 10:00 AM, Jaybird180 said:

Thanks for the suggestion to re-read some material. I'd come to that same conclusion as I began thinking this through on my way to work this morning. I do need to talk through some things as I read and also some thoughts:

  1. In Ch 2, the section on throttle control, one of the margin comments mentions that it's possible to get on the gas too early and cause the bike to run wide. In light of my new understanding of what the rear does in a corner, in that it's the dissimilar circle size on the side of the rear tire that causes the bike to turn I now ask :does the (greedy) application of throttle really cause a bike to run wide while leaned over? We already have observed that we can lift the front with throttle and the bike will remain as sure as if on rails.
  2. Ch 2 also give the reason for the idea behind the 60/40 and that it's based on a comparative measurement of footprint, nothing more. 0.1-0.2g of throttle is what's needed to maintain that relative contact patch. But since we now understand that size of contact patch isn't the determining factor in available traction should maintenance of footprint still be a Primary concern as requested by Ch2?

I'd like to make a note here: I'm not advancing an idea of "whacking" open the gas, nor am I saying that a smooth roll-on isn't the right thing to do. I am saying that perhaps we needn't be as gentle with the throttle as I previously thought. If this is really the case, then perhaps I opened a door for more available attention for other things. I hope I'm not opening the door to more highsides.

    3. Donny Greene in his comment at the end of Ch 3 says it this way: "Once you have the throttle control rule firmly understood and practiced and you can get the rear wheel spinning with a smooth roll-on, your bike will handle again." What if instead of spinning the rear, you time your roll rate so that the tire is hooked up and driving forward? I can see a viable reason to want to use a spinning rear wheel to help finish the corner, but it might be too much mid-corner even if it does work just fine for Casey Stoner.

1. The bikes want to follow a straight line, if they can, if not forced otherwise (remember the Newton's law we described priorly?).  A sphere rolling on a flat surface can't make a curvilinear trajectory.  A disc (like a coin or a tire) can, if rolling over the same flat surface off a vertical position (leaned).  For keeping that leaned attitude, someone or something must have initiated the leaned rolling.  The Newton's law manifests itself in the case of the rolling leaned disc, however, there is a force making the disc deviate from the straight trajectory, turn instead over a circle: a portion of its own weight constantly pulls the disc towards the center of that disc.  Same force is what keeps the motorcycle leaned and turning in that out of-the-curve wheelie. 

If that centripetal force (portion of the weight) equals the centrifugal effect of the circular movement, the bike as well as the disc will keep describing the same circle over and over again.  Yes, your wheeling bike will keep turning even after the end of the curve (you must put your front tire down and counter-steer to decisively straighten the trajectory up).  

If that centrifugal effect becomes bigger that the centripetal force (portion of the weight), then the bike tends to open the circle (to constantly increase its diameter).  That is what makes a leaned bike that is excessively accelerated (greedy application of throttle) run wide and subsequently reduce the lean angle.  That is also the reason that the leaned and turning bike in that wheelie will tend to return to a straight trajectory, if enough acceleration and time is provided.

2.  You could accelerate harder than 0.2 g, let's say 0.9 g and achieve 10/90 weigth distribution.  Consider that your rear contact patch will be loaded with harder longitudinal forces (exactly 90% the magnitude of the combined weight of your bike and your body, because F = mass x acceleration).  If the rubber of your good racing tires is able to achieve traction of 1.1 g, then, your rear tire can only deal with around 0.3 g of cornering lateral force (around 20-degree lean).  Then, you will be forced to slow down to prevent a slide (like riding on wet-dirty pavement).  There it goes your excess of acceleration due to the need to moderate your speed.  Even if you make the turn in those conditions, you will only have a fraction of the grip that you could have in the front contact patch (only 10% of the weight on there, remember?) for countersteering out of the turn.

3.  Let's do some math: Sustained acceleration of around 1.0 g (32 ft per second or 22 mph of additional speed per each second in the curve) will give you a nice sustained wheelie.  If the limit of available traction allows a maximum speed of 80 mph in that curve, that will be your leaving or exiting speed.  If it takes 3 seconds to complete the curve in the described conditions of strong acceleration, your maximum entering speed must be 80 mph - (22 mph x 3 seconds) = 14 mph.  Your average speed through the curve would be (80 + 18) / 2 = 49 mph.  Another rider following the recommended 40/60 weigth distribution (acceleration of 0.1 g) would increase the speed at a rate of 2.2 mph per each second, which means same exit speed of 80 mph and entering speed of 80 - (2.2 x 2 seconds) = 75 mph, being his average speed of 77 mph.  Note that he used 2 seconds while you used 3 seconds (gross approximation only).

Hope those numbers help you see the dramatic difference.  There is more than maximum available traction involved in this picture of moderate or recommended weight distribution: steering, suspension, tire performance, stability, as mentioned in my previous post.

Practical considerations: You want to keep your steering tire loaded with a decent amount of weight or available traction.  To force a speeding heavy bike in and out of a lean angle requires muscular effort and a solid fulcrum, which is a gripping front contact patch.  That loaded front tire can save you in an emergency swerving and in a slide of the rear tire.  Imaging going through a quick chicane with only 10% of the total weight on the front tire? 

Please, excuse my long post.  :huh:

 

  • Thanks 1
Link to comment
Share on other sites

@Lnewqban I love the way you explain things. It often takes discussions to basic math and physics and that's a good thing as it leaves rider error out of the discussion. If you don't mind, I'd like to make an observation in the hopes that it will untangle this discussion.

In order to turn a motorcycle (at speed) it has to lean. Agreed?

If this is true, the act of leaning and turning are 2 separate behaviors and are about different planes of motion. The leaning would be a roll about the longitudinal axis and turning would be a lateral movement or yawing motion about what is often referred to as Z- Axis. But these are still 2 separate changes of state of motion. Agreed?

Secondly, Speed through a turn DOES NOT (by itself) make a turning limitation. Controversial, I know....

I'll go on record as saying that because there is a limitation to how far the bike can be leaned, there is also a limitation to how much pressure can be applied to the road/tire meeting point and therefore the tire will slide as we approach the limits of current technology. I think the math used in example #3 has a very limited circumstance where it applies, but I get your point in that it would be the losing way to negotiate the corner in your example. To do the math backward to limit the entrance speed would be a good example of what happens with a ham-fisted rider - he'd cause all types of problems with low entry speed and trying to make it up on the gas...

I'm just asking the question: if tire traction is stable, and we take the same line, same entry speed, get on the gas at the same point but instead roll it harder, sufficiently enough to lift the front will we have gained a better result. I think, yes. And if this is true, why do we need to be concerned with limiting our roll on while respecting tire traction limitations?

 

Link to comment
Share on other sites

On ‎12‎/‎15‎/‎2017 at 4:51 PM, Hotfoot said:

If so, I stand corrected, what lean angle are we talking about? 

Wish I could find some footage. I don't think it was dragging elbows as he's (Marc Marquez) known for but yet still significant. In the OP I linked to a request from Cobie to find footage of Schwantz doing similar. His recollection was 35-40 degrees.

Edited by Jaybird180
Accuracy
Link to comment
Share on other sites

On 12/19/2017 at 6:03 AM, Jaybird180 said:

@Lnewqban

Secondly, Speed through a turn DOES NOT (by itself) make a turning limitation. Controversial, I know....

 

It sure does - I can scrape the pegs doing a full lock U-turn or circles in first gear. You cannot do a full lock turn at 200kmh, and certainly not around a traffic cone like I can in a carpark.

 

On 12/19/2017 at 6:03 AM, Jaybird180 said:

@LnewqbanI'm just asking the question: if tire traction is stable, and we take the same line, same entry speed, get on the gas at the same point but instead roll it harder, sufficiently enough to lift the front will we have gained a better result. I think, yes. And if this is true, why do we need to be concerned with limiting our roll on while respecting tire traction limitations?

 

"A better result"? Does that mean lower lap times?

Link to comment
Share on other sites

On 12/19/2017 at 6:05 AM, Jaybird180 said:

Wish I could find some footage. I don't think it was dragging elbows as he's (Marc Marquez) known for but yet still significant. In the OP I linked to a request from Cobie to find footage of Schwantz doing similar. His recollection was 35-40 degrees.

35-40 degrees is nowhere near max lean angle. MM93 is getting 67 degrees of lean angle - I find it very difficult to believe you could wheelie under power at that lean angle as most of the power is being applied laterally. If you tried you would be at high risk for a highside IMO

Link to comment
Share on other sites

I had a day many years ago of trying to spin up the rear at full lean. I wasn't able to get the tire to break traction. In hindsight, I may have been in too high a gear, though it seemed right for the drive out of the turn once the bike was vertical.

  • Thanks 1
Link to comment
Share on other sites

54 minutes ago, Jaybird180 said:

I had a day many years ago of trying to spin up the rear at full lean. I wasn't able to get the tire to break traction. In hindsight, I may have been in too high a gear, though it seemed right for the drive out of the turn once the bike was vertical.

You weren't going fast enough then ;)

Link to comment
Share on other sites

On 12/18/2017 at 3:03 PM, Jaybird180 said:

.......I'm just asking the question: if tire traction is stable, and we take the same line, same entry speed, get on the gas at the same point but instead roll it harder, sufficiently enough to lift the front will we have gained a better result. I think, yes. And if this is true, why do we need to be concerned with limiting our roll on while respecting tire traction limitations?

 

Please, excuse the math and the physics; it was just an attempt to show and quantify the limits that we are dealing with in this discussion.

Allow me to insist on some basic concepts, which are very important for you and for any rider to visualize and understand in a clear and solid way.  You should know and apply these things without thinking too much about them while riding a fast motorcycle in a proficient way.

The limit to "roll it harder, sufficiently enough to lift the front" is the available traction of the rear tire in those cornering conditions.

If you can do it without inducing a slide of the rear tire, it is only because your tires have not been loaded enough (with cornering speed) in the previous stages of cornering: your entry speed was lower than it could have been.  In other words, you will be trying to compensate a slow entry with a fast exit.

Why is that?  I believe that this is the point that unfortunately I have failed to explain properly.

Hence, I will try the questioning approach, hoping to make you see some limits:

1) Would a unicycle corner better that a bicycle?  Why?

2) Do you believe that a motorcycle doing a wheelie becomes a motorized unicycle?  Please, explain.

3) What limits the maximum speed at which a sport motorcycle can negotiate a turn of 200-foot radius?  How does rain affects that?

4) What forces are acting over the contact patches of a bicycle that is cornering and simultaneously coasting?

5) Regarding turning a motorcycle along a corner, should the lean angle be considered a consequence or a cause? Please, explain.

6) What causes a wheelie (for a vertical attitude of the bike)?  How can it be controlled?  Why?

7) What forces are loading each contact patch during a wheelie?

  • Thanks 1
Link to comment
Share on other sites

1 hour ago, Lnewqban said:

Please, excuse the math and the physics; it was just an attempt to show and quantify the limits that we are dealing with in this discussion.

Allow me to insist on some basic concepts, which are very important for you and for any rider to visualize and understand in a clear and solid way.  You should know and apply these things without thinking too much about them while riding a fast motorcycle in a proficient way.

The limit to "roll it harder, sufficiently enough to lift the front" is the available traction of the rear tire in those cornering conditions.

If you can do it without inducing a slide of the rear tire, it is only because your tires have not been loaded enough (with cornering speed) in the previous stages of cornering: your entry speed was lower than it could have been.  In other words, you will be trying to compensate a slow entry with a fast exit.

Why is that?  I believe that this is the point that unfortunately I have failed to explain properly.

Hence, I will try the questioning approach, hoping to make you see some limits:

1) Would a unicycle corner better that a bicycle?  Why?

2) Do you believe that a motorcycle doing a wheelie becomes a motorized unicycle?  Please, explain.

3) What limits the maximum speed at which a sport motorcycle can negotiate a turn of 200-foot radius?  How does rain affects that?

4) What forces are acting over the contact patches of a bicycle that is cornering and simultaneously coasting?

5) Regarding turning a motorcycle along a corner, should the lean angle be considered a consequence or a cause? Please, explain.

6) What causes a wheelie (for a vertical attitude of the bike)?  How can it be controlled?  Why?

7) What forces are loading each contact patch during a wheelie?

That's the point where you've made it clear.

  • Like 1
Link to comment
Share on other sites

1 hour ago, Lnewqban said:

 

Hence, I will try the questioning approach, hoping to make you see some limits:

1) Would a unicycle corner better that a bicycle?  Why?

2) Do you believe that a motorcycle doing a wheelie becomes a motorized unicycle?  Please, explain.

3) What limits the maximum speed at which a sport motorcycle can negotiate a turn of 200-foot radius?  How does rain affects that?

4) What forces are acting over the contact patches of a bicycle that is cornering and simultaneously coasting?

5) Regarding turning a motorcycle along a corner, should the lean angle be considered a consequence or a cause? Please, explain.

6) What causes a wheelie (for a vertical attitude of the bike)?  How can it be controlled?  Why?

7) What forces are loading each contact patch during a wheelie?

  1. The rider's position on a unicycle means that the rider must exert more force on the single tire whereas on a bicycle the outstretched rider can use both tires.
  2. Yes because the motorcycle is turning about the rear wheel's circumference
  3. Centripetal force. In the rain we cannot get the same level of friction from the road surface and therefore cannot generate the same load safely.
  4. I'll give this some thought and come back to this one if you don't mind as I believe that bicycles don't quite behave the same as motorcycles due to the bicycle having similar tires on front and rear....Okay I've thought about it- It's centripetal force
  5. Lean ange is cause. See #2
  6. Excessive acceleration. Controllable by modulating the acceleration until Balance Point (BP) is reached, afterwards it's subject to the laws of gravity if BP is exceeded
  7. Gravity and Engine power is forcing the rear wheel into the ground, until a certain angle as determined by swingarm angle and wheelie angle, which might constitute the Balance Point
  • Like 1
  • Thanks 1
Link to comment
Share on other sites

1) "Would a unicycle corner better that a bicycle?  Why?"

A unicycle steers more sharply than a bicycle because of the bicycle's wheelbase. Of note is that the unicycle is countersteering and propelling from the same tire.

2) "Do you believe that a motorcycle doing a wheelie becomes a motorized unicycle?  Please, explain."

Not exactly. See #1. The wheelied motorcycle at speed, arguably because while it can "wobble" left or right, it cannot be accurately steered. The motorcycle must come back down to be countersteered from the front wheel.

4) "What forces are acting over the contact patches of a bicycle that is cornering and simultaneously coasting?"

Jaybird mentioned centripetal force. Then there is the vertical component of the rider & bicycle weight. In this situation the friction on the bicycle tire contact patches is extremely small. I am most curious about this particular question and what we are supposed to understand from it. 

5) "Regarding turning a motorcycle along a corner, should the lean angle be considered a consequence or a cause? Please, explain."

I am thinking that "corner" in this case refers to a given, fixed path. If yes, for a given path on a given motorcycle at a given speed the lean angle is a consequence. I am not sure if I read this or came up with it in isolation: On a centrifuge I think of the arm that connects the motor and test tubes as the friction of the tires. The angle the tubes will take is a consequence of the motor speed, the arc, and the weight of the test tubes. Just the same I think of the motorcycle lean angle as a consequence of the speed, weight, and corner arc.

  • Like 1
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
×
×
  • Create New...