[caption id="" align="alignright" width="300" caption="Image via Wikipedia"][/caption]
With the introduction of cut springs we begin our dive further into the complex concepts of suspension.
There are numerous workings of suspension, but if you are ever in doubt, refer back to the tires. You may have clued into this long ago, or perhaps it's just crossing your conscience now, but tires are the only part of the car that touches the road. When racing, no matter the form, you must always be conscious of the tires and what they are doing. This here is your sight into the control and actions of your vehicle.
So you want to go fast? Well, let's define speed in relation to automobiles; It's a increased rate of travel over a drivable surface. Nothing to complex, the idea that your traveling at a great speed over a road or terrain, so what does this have to do with tires? They are the single most important part of your car, the tires are your control points, they touch the road and are your only control of motion. Tires are heart of speed, controlling acceleration, braking, turning and all combinations of these 3 states of motion. By changing the characteristics of tires, you change the funtion, feeling and albeit, speed of your vehicle.
What you plan to do with the car is the hardest decision, but the most important. The purpose and usages of the vehicle will determine the tires used. It's a bit of an odd, but direct process. Many people buy a car, with no direction, throw modifications at it, and hope for the best. Let's get you pointed in the right direction. The endurance, terrain, speeds, rates of acceleration, braking, weight transfer all affect the tire choice, not forgetting the rules that dictate your racing, if any. Let's talk examples; Drag racing is a great example of purpose built tires. Both the driven and non-driven wheels of a Drag car are vastly different, those driven use very soft, flexible and wide tires. The non-driven ones are often very skinny, hard and thin. What are the reasons for this?
Tires manage those 3 characteristics mentioned above; acceleration, braking, turning. A large majority of drag racing cars are rear wheel drive, let's continue our example with that in mind. The rears are very soft, balloon like even, and extremely wide. The purpose for this is a complete dedication to forwards acceleration. When talking tires, there is something everyone must known, even everyday drivers: Contact patch. Tires are flexible rubber cylinders, filled, usually, with air. When weight is placed upon a tire, it deforms and creates what is called a Contact Patch. This patch is pretty simple to understand, depending on the shape of the tire and the amount of weight placed on it, and air inside it, there is a square or round section of it touching the ground. Picture taking a balloon and pressing it against a wall, the part of the balloon touching the wall will squish flat, in a circular patch, the tires on your car do this too. The tire patch can roughly determine the amount of 'grip' it has. The greater this tire patch is, the greater the amount of grip on a dry road surface. With that in mind, let's get back to our example of Drag racing tires. The large rear tires are very balloon like, they are often filled with a very low pressure of air, are wide and made of a soft rubber material. This creates a gigantic tire patch on the track! The idea of this huge tire patch is to create more grip than the engine can overcome. If the grip is too little when the power is delivered aggressively to the tires, they will slip and spin in place, the car will remain at rest even momentarily and reduce it's speed of acceleration.
The front tires of a drag car are quite the opposite, skinny, and very hard, the purpose of the drag racing car determines it's tire needs. Since the vehicle doesn't need to steer very much, but needs to travel fast down the track, the front wheels are as minimal as possible. Their skinny width offers three advantages: a small contact patch, very little aerodynamic drag, and light weight. Why would someone want a small tire patch? In the case of drag racing you want to accelerate and travel as fast as you can, any way you can reduce resistant to movement the better! This small tire patch, and hard rubber compound with high pressure, create a small tire patch. Like mentioned before, on a dry pavement surface this small tire patch is very little resistance.
How does this apply to other motorsports? It's rather simple really, you want to manage the amount of grip you need. In most cases there is a need to increase grip, in others, just simply to manage it well. Let's dive into something a bit more complex in terms of thinking about tires. Grip racing, be it auto cross, road courses, hill climbs, rally racing, oval racing etc. They all want to maintain a high level of grip. The separation in tire design is determined by the surface; there's dry pavement, and then there's everything else. In any of these usages, accelerating, braking and turning as fast as possible is the most important.
Dry pavement is rather simple to understand, much like drag racing, the surface of the tire is designed to create the greatest amount of contact patch possible, while keeping the resistance to rolling at a minimum. The only complexity to optimum dry pavement driving is to create this great tire patch, and retain it with as little roll to the tire during cornering. Cornering is a tricky subject, but let's tackle it. Remember as mentioned earlier that when weight is transfered to a tire it deforms? This is very true during cornering. Imagine two balloons, one in your left hand and one in your right hand. They are pressed against the table in front of you equally. If the two balloons are of the same size and air pressure, then the contact patches created by their interference with the desk are equal. This is the expected result of driving in a straight line. Now what if you had to make a right turn, what happens then?
Let's introduce the difficulty of motorsport, the very cause of all our problems; there is a law of physics which states: An object in motion tends to stay in motion. What does this mean? It's rather easy to explain. A big round rock, if sitting still, wants to stay sitting still. It takes a lot of effort to push it and get it moving. Now that it's moving stopping it is very difficult, it wants to continue moving forever, if there is nothing to resist it's movement. Changing it's direction is equally difficult, it wants to keep rolling in the original direction it was pushed and resists changing to it's new direction. That rock is your car. Your car is big and heavy, it will resist any changes to it's motion as much as possible! So how does this affect our cars when cornering?
Back to the Balloons, you've got one in the right and one in the left hand, pushed against the desk equally, you are driving straight, creating equal contact patches. You want to turn right, what would your car do in this situation? It would want to continue moving straight, resisting your input to turn! You begin to turn right, the car wants to contiune going straight, so what happens? The car tries it's best to not turn, by leaning its weight away from the inside of the turn. The car will lean, or 'roll' away from the turn. In this case the car is leaning to the left during your right turn. Your body inside the car does the same thing when driving. So what happens to the balloons? Well the weight of the car is now leaning left, so there is more weight on the left balloon, and less on the right. The balloon on the left will now deform more, becoming a bigger contact patch, and deform less on the right side, making less of a contact patch.
Great! This helps the car turn around a corner, it now has more grip where the weight is placed, helping point it in it's new direction. What can go wrong with this? Sadly tires are not round balloons, they work similarly, but are not quite shaped the same, also the affect of the tire patch increasing isn't an infinite concept. There are ways to add too much weight to a tire, and too little to a tire to create a loss in traction in both cases.
The tire is a cylinder shape, and although this isn't the most ideal shape, it's the most common. Overloading and underloading tires is a big problem in racing, too much weight can cause a tire to deform so dramatically that the contact patch begins to actually reduce. The speed of weight change also affects the grip, if you turn to suddenly it will overload the tire even more dramatically and traction will break. Underloading is a bit easier to understand, as mentioned before, as the weight is removed from the tire, the contact patch becomes smaller, creating less grip.
The next complication to the idea of grip is that of soft and/or moist terrain. This creates a very difficult factor in tire design. For when there is water on a roads surface, tires are designed to push water out of the way, if you were to use a flat tire, with no grooves in it, the contact patch created would be flat. This contact patch would sit on top of the water, rather than touching the road itself. The water becomes a lubricant for the road and tire contact patch making the car slide along the surface. This does not promote any changes in direction or momentum, it does not allow acceleration, deceleration or turning. Rain tires are designed specifically to push and slice through this layer of water resting on the road surface, and have the rubber touch the pavement directly. This removes the water as a lubricant, but creates a new problem: The contact patch is now much smaller. Only small bits of the tire is touching the road surface rather than the complete contact patch, it is a trade off, and one that still isn't mastered yet even with today's modern design.
Mud, sand, gravel, snow, all offer their own unique challenges. The interesting thing lies in the contact patch as well, it's no longer flat. The surface is much more dynamic, it changes at either a faster or slower rate than the tire deformation from the weight of the vehicle. Much like rain tires, these surfaces require groves, however it's not quite to allow the tires to reach the road surface. In most cases there is no road surface below, these grooves work similar to a paddle in a boat, providing a surface to push off from. Sand rails are a type of sand dune vehicle, they are the most aggressive example of this. They use small scoops on the driven wheels to push the vehicle forwards. General off road tires, both have similar paddles, but also use hard edges to aid in climbing up harder rock surfaces. Snow racers use skinny tires with metal studs. While the skinniness of the tire allows it to sink deep into the snow, it also acts as a rudder through the wet, thick snow, while the metal studs reach the ice and frozen ground below.
You need to pick your tires for your usage, for the most part most of you reading this will be driving on paved roads. What's the next step from here? We've established the importance of tires, the next is the suspension. This is what determines the transfer of weight. Your car will transfer weight during our listed three changes in motion. Back to the Balloons.
We've talked about the changes in contact patch during cornering, but these changes happened during acceleration and deceleration as well. Let's add to the demonstration, 2 more balloons. So now we have 4 Balloons, 2 for the front, 2 for the rear. We know how weight transfers left to right, this is from a change in the vehicles motion, we were trying to turn the car while it was moving. This transfer leaned weight away from the direction we were turning, this is because the car wanted to stay in a straight path of motion. This safe effect occurs during acceleration and deceleration. When at a rest or moving slowly, pressing the accelerator results in the car trying to increase it's speed, this is a change in it's motion. The car wishes to remain at it's current speed and direction, and as you speed it up the weight resists this change. Upon accelerating the weight shifts towards the rear of the car. Picturing your 4 balloons and their contact patches, you can imagine the rear balloons receiving more weight, increasing the size of their contact patch and the fronts reducing their held weight, reducing the size of their contact patch.
Suspension is the control of weight transfer, without it the ride quality to be very harsh, and on rough surfaces the car would be unpredictable. The purpose of suspended wheels is to allow them to touch the ground as much as possible, no mater how rough or uneven the surface is. There are two very active parts of your cars suspension, the spring, and the shock. Each has their job, and each is very important to the other. The springs job is to carry the weight of the car, if it is to hard, the ride is to harsh, often overloading and underloading the tires very quickly on rough or sudden changes in the road surface. If it is too soft the car sags and becomes to low, having difficult clearing uneven road surfaces, small objects and/or completely compressing the spring. This is a solid state. The weight and usage of a car determines it's spring capacity. Shocks are the second part of this equation, they work with the spring, not to hold the weight of the car, but rather moderate the speed at which the spring compresses and decompresses.
Imagine if you will, stretching an elastic band between your two hands. If you let one end go, it will snap you in the hand, but if you slowly move your hands back together, you can return the elastic band back to it's original state without any sudden changes. This is the purpose of the shock, to control the speed at which the spring moves. The shock has to control the spring moving in two directions. The spring can compress quickly, as well as decompress quickly, the shock has to control both, and in most cases does so at different rates. The rate of control when the spring compresses is called "bound". This resists the spring compressing too quickly, perhaps hitting a bump in an otherwise smooth road, without the shock the wheel would shoot up into the wheel well, and for a moment, no longer touch the road. The resistance, or control of the springs decompression is called rebound. This keeps the spring from suddenly expanding. Having no shock would result in the car lifting quickly, again removing weight and perhaps removing the wheel from the road. In either case, this unsettles the car and makes the handling very unpredictable.
Although that is not new information from the previous cutting springs article, it's useful to remind you of the dynamics of suspension. Essentially the car floats on the springs while the shocks control the speed at which the weight transfers. Motorsports is the control of this weight, utilizing the weight transfer when needed and minimizing it when it is unwanted is crucial to the success of speed. This is all to control the size and shape of the tire contact with the road, that's the sheer purpose of suspension design. When ever you are thinking about changes to the suspension, refer to the tires, how they are contacting the surface, and be aware of what they are doing, as that will answer your questions.
How do we go deeper? I realize above is a simplified version of contact patches and how suspension affects tires. You are now aware of the basics of weight transfer. How else can we control it? What else affects it? Let's work into some theories and ideas further from these.
Let's cover some other ideas of suspension. Sway bars are an interesting and very overlooked dynamic of suspension. One of our earlier examples had us reviewing that of the contact patch of our balloons during cornering. We realized that during a change in direction, that the tire on the outside of the corner receives the most weight. On a right hand corner the car leans to the left to try to continue straight, and vice versus on a left hand corner. With our knowledge of springs and shocks, we could increase the resistance of the springs and change the rates of the shocks to help reduce this problem. We would be adding higher resistance springs, and changing the rates of the shocks to match to help resist the weight transfer. The more we can keep the weight equal on all 4 tires, the more greater the amount of grip, and the faster the car travels around the corner. In order to make up for this 'roll' without changes to the car, we would have to slow the speed of the car through the corner. This would give the weight of the car less momentum to carry in it's current direction. This is not acceptable for racing. So we can stiffen the suspension to resist transfer during corners, however, what if we are running over rough surfaces? We don't want the suspension too stiff when going over rocks or very bumpy roads, our tires won't be touching the ground very often.
There's a cure to this problem, sway bars are a common part on most cars, but a majority of people don't know about them. A sway bar allows the suspension roll left and right, to be tuned separately of that front to back roll. A sway bar is a 'U' shaped bar made of spring steel. It stretches from the left wheel, to the right. The center of the 'U' is affixed to the bottom of the car. The bar can pivot freely on these mounts, but only in one direction, the ends of the bar can only rotate up and down. One end of the bar is affixed to the left wheel, the other to the right. As one wheel lifts up, compressing the suspension, the end of the bar moves up. Since the other end is attached to the other wheel, it too tries to lift the suspension up. This resistance is interesting. As the suspension compresses on the left side during a right hand corner, the suspension on the right side would normally decompress because of the weight leaning the car. However, now that the sway bar is in place, as the left compresses, the right tries to compress as well. This basically makes the suspension 'twice' as stiff when the car leans left to right, but when the left and right wheel compress together, the suspension is it's original stiffness. For most cars there is a front sway bar, and a rear sway bar. The complication to this ideal is that sway bars are designed to flex. They are made from spring steel and allow flex depending on their rate of resistance. This is the adjustable factor of them, that resistance of weight transfer can be increased or decreased depending on purpose, and it can be done individually to the front and rear wheels.
Another factor to consider when thinking about contact patches, is something that came to production vehicles only in the last 20 years. It's that of active, or changing camber. Camber, if your new to suspension dynamics is a direction that a wheel leans. Cars do not always have straight up, perpendicular wheels, rather if you look down the side of some vehicles, you'll notice the at wheels actually lean in. This change in wheel angle is called Camber. More and more modern cars are being sold with negative camber. Negative camber is when the top of the wheel leans into the car, this is an interesting concept all on it's own.
It is accepted that regular everyday cars lean when cornering. The compromise made to allow an average car to travel on all sorts of road surfaces as comfortably as possible results in a very soft suspension. Many years ago, cars like the Volkswagen Beetle and Citroen 2CV had no camber correction for their roll. Follow along closely; the movement of a cars suspension is called 'travel', as the wheel moves with the suspension from it's fully decompressed position to it's compressed position, older cars like these, the wheels moved straight up and down, parrallel to the body at all times. When driving around a corner, the car would lean, inside wheels having less weight, and outside wheels having more, the wheels would lean with the car as they would always stay parallel to the car. This caused problems for the tire, as it now was riding on it's side, creating a small or unpredictable tire contact patch. This made the handling of them very poor as the tires were not designed to have an even contact patch at all times. Newer cars have remedied this problem, as the suspension compresses and the wheel moves up into the body, it begins to angle, changing camber. This keeps the bottom of the tire parallel to the road, making an even and consistent contact patch.
A newer car, as it rolls to its side during cornering leans, the inside tires begin to gain positive camber as the car leans away from them. This means the top angles away from the car, while the tires on the outside of the car, as it leans towards them, begin to lean in. Basically keeping the wheels parallel to the road.
In order to go fast in your car focusing on maintaining a consistent and even contact patch on each is crucial! Is there any other ways improve the consistency of the tires contact patch? Yes! Let's dive into the concept of 'Roll Center'. If you remember from physics class or just screwing around with rulers, or any long bar, you'll know of the feeling or idea of 'leverage'. Leverage is the increase of force over distance, leverage multiplies the input of force. For example, trying to undo a bolt or nut with a very short length wrench is much more difficult and takes more force, then undoing that same bolt with a longer wrench. The longer wrench multiplies the input force, errr makes you more manly. A car's roll center is a very similar idea.
The way your car interacts with the world and physics can be simplified down to the shape of a triangle. Before we dig in, I want you to know, this is still very much a beginners guide to understanding suspension dynamics, the simplification of 'roll center' to a triangle concept is very basic, and there is much learning to seek beyond this ideal. Each car is different and has many different factors affecting roll center. With that in mind, do indulge in the concept of this triangle as we dive in.
So what is this triangle? Much like the balloons, it represents something. When facing your car directly from the front or rear you can picture this triangle super imposed on the vehicle. The upper point being the floating weight of the vehicle, the lower points being the left and right contact patches of the left and right tires. If it helps grab a pencil and paper and draw as you follow along.
Let's begin with an equilateral triangle, that means all the sides are the same length. If you were to try to push this triangle over, it would be very stable, difficult to push over when pushing at the top point. This is a fairly neutral center of gravity for the car, this upper point represents the leverage the weight of the car has over the points in which it will pivot over. If you were to raise the top point of the triangle, without widening the distance between the two lower points, you would have raised the cars center of gravity. This gives the weight of the car more leverage when it tries to roll to the side during cornering. If we remember correctly, leverage multiplies force, so the amount of force the weight of the car is placing on the outside tire during cornering has dramatically increased. Inversely the weight on the inside tire during cornering has dramatically decreased. We are now in a situation to overload one tire and underload another, making the car handle poorly, having to lower our speed through a corner in order to navigate it safely.
However, let's tackle the other extreme, we lower the upper point of our triangle. Now the center of gravity is very low, reducing the amount of leverage the car's weight has when it transfers/leans to the side during a corner. It's obvious that this helps reduce the unequal distribution of weight to the inside and outside tires during a corner. The car will roll less, the inside tire will loose less weight, helping avoid under loading the tire, keeping the contact patch larger. The outside tire will now receive less weight, allowing the tire contact patch to still grow, but helps avoid overloading the tire and deforming the contact patch. This effect allows the car to travel at a faster rate through a corner. This is speed
While we are on the the triangle example, let's look at the two bottom points of the triangle. What can we do to further aid this roll center reduction? Well, we can move them out, away from the center of the car. Much like our talk on leverage, these points offer counter leverage, as the road is a solid object that the car pushes against. The shorter we make the leverage of the car's center of gravity, and the more leverage we give to the points of contact with the road, the less the car will roll. This is the idea of 'flat cornering', it is the ideal situation for a majority of grip racing drivers. Faster speeds through the corners means less time is spent braking into the corner for a slower speed through it, and less time accelerating to regain the momentum the car had before the corner.
Constantly fighting with our law of an object wanting to stay in motion, these are your tools to combat this affect when dealing with acceleration, deceleration and turning. Now roll center is a much more complicated topic than this, please let this be a stub of information in your brain, that I highly suggest seeking greater clarity. You'll find as you dive deeper into this topic you'll learn that it is very specific to each car, and not just a specific model, but rather each and every car is different because of all the factors that weigh in to measure a roll center. Things like tire flex, suspension geometry, vehicles weight placement, suspension specifications, etc all have large and small affects on the roll center of a car, and depending on your motor sport of choice and desired car feel there are times were you want to allow the car to roll, and times when you do not, with separate consideration to the roll and dive of the front in relation to the roll and squat of the rear.
How do I apply this knowledge? This is a basic guide to understanding your suspension, it is up to you to decide the vehicle you wish to use for what purpose and to learn about what can and can't be done with that vehicle with the best methods possible. However, you can use this information to begin understanding what is called your 'Butt Dyno'.
A joking term related to people trying to guess the power of their car based on the immeasurable 'feel' of a cars performance. However, it is actually very crucial to your daily life and racing life. With this new found knowledge of what a car is doing during acceleration, deceleration, cornering, and all combinations of each let's look at your dyno.
The tires and how they are contacting the road is the most important thing to pay attention to when driving a car. Being aware of all 4 tires and their state of grip allows you to understand how to improve your driving, this is your translator to the limits of the car. This translation tells you when you are at maximum and minimum adhesion to the road surface, and when you have lost adhesion. The complexity of this idea is that each tire is receiving different inputs and forces at almost all times, whether slight or great. If we go back to our idea of balloons, we last left off with 4 balloons. We have focused on the changes in weight placement in regards to transfer of weight from left to right, and from our last example front to back. Now we must consider the combination of the two.
Driving a car is not a static action, it's not like playing Mario where you can build a routine, rather it's a series of actions and corrections, projected movements followed with the reactions of the input. The state of a cars motion is nearly never neutral especially during racing. You are always accelerating, decelerating and turning, in combination with each other to attempt to be at, but not go past the limit of adhesion of the tires at all times. Let's picture our 4 balloons.
Two represent the front tires, two the back, both having a left and right. These are the tires on our car. When first accelerating our attention focuses on the driven wheels of the car, the wheels that receive power from the engine. We are trying to accelerate as fast as possible and depending on the power of the car and it's setup to deal with this power, we must pay attention to when the wheels begin to slip. We have multiple inputs in our car, the gas pedal, the brake pedal, clutch and shifter depending steering wheel and hand brake. When accelerating in a straight line we are generally focused on the gas pedal. Our job is to deliver as much power to the driven wheels as possible without overcoming their level of grip. If they begin to spin we will loose acceleration, letting back on the pedal until we find traction again allows up to continue accelerating forwards as fast as possible. This is a rather simple concept.
During braking we are paying attention to the state of the wheels grip, especially those at the front of the vehicle. Weight is being transfered to the front of the car, our two front balloons are gaining contact patch, which is good, but they can be overloaded resulting in a loss of traction. We need to feel this in the car, our foot controls the pedal which is braking, by letting off lightly when the tires begin to lose traction we know we've past our limit.
The thing is, with racing cornering is always combined with decelerating and accelerating. So Perhaps we are slowing down when we enter a corner. For the sake of examples we'll make it a right hand corner. As the car slows the weight shifts to the front, but because we are changing the direction of the car to travel to the right, the weight of the car also shifts to the left. If we were to look at our 4 balloons, you'd notice that the front left is the most compressed and the rear right is the least. Weight is shifting both forwards and left, as a driver we must feel when the front left tire is reaching it's limit of adhesion, as it's the most important to this change of direction and momentum since it's received the most weight. If it loses traction the job of the front right and rear left tire now need to make up for it, often they cannot as they do not have enough weight to create the traction needed to support this sudden transfer of responsibility to them, and begin to slip too. This whole situation is dealt with by being aware of the state of the tires. Feeling the weight transfer and knowing where it transfers to allows you to monitor the change in direction and feel if it is successfully changing direction or remaining in it's original path. If the car loses traction and rather than turning, slides straight, this is called 'understeer'. The car is under performing it's duty of steering.
Right after this process of deceleration during turning at the entrance of a corner, is followed by the exit of the corner. Leaving a corner means you need to accelerate as fast as you can to get to the next corner. This is a whole new complication to the transfer of weight. You now have a majority of front weight on the front left wheel, and need to continue turning through the corner, but by accelerating you will transfer weight towards the rear of the car. Looking at our 4 balloons again, our front left has the most weight, where our rear right has the least. The front right and rear left are approximately equal for simplicities sake. Moving our foot from the brake to the gas causes a change in weight, the car now wants to shift the weight to the back while turning. This causes a reduction of weight on the front left and moves that weight now to the rear left. If we are looking at our 4 balloons, the rear right has the most squish, where the front right has the least, the front left and rear right now being roughly equal. In this case, under steer is still possible, depending on the drive type of the car and it's power to accelerate, as well as it's setup, the car can push outwards, away from the center of the corner, because the wheels that steer are underloaded and/or receive to much power and spin. Another problem is the opposite of under steer; over steer can occur, this is when the inputs of the vehicle cause the rear wheels to lose traction during a corner. This is an opportunity for the weight of the car to begin to drift outwards trying desperately to make the weight of the car travel in a straight line, away from the inside of the corner. This often will result in a spin as the front wheels still retain traction, creating a point for the rear to pivot around.
Controlling understeer and oversteer is done through awareness of the states of grip the tires have, and understanding what tire(s) have lost traction and why. It is something that comes as a gut reaction with practice. there's no thought, much like the smell of an apple you recognize it instantly and make changes to correct it without hesitation. Developing these reactions as a habits is not difficult, even in regular daily driving you can be aware of the contact patches of ones tires even if the car is not at it's limits. Soft, sloppy cars are the best way to observe these states of change to the tires and their contact with the road, simply because the cars actions are very exaggerated and easy to notice. Walking is an odd but interesting way to observe it, paying attention to the contact patch of your shoe when walking, you can actually feel the interaction of the pavement and shoe with your foot. There's much etcetera to these examples. As you practice, you begin to refine your observation skills, improve your feeling of motion increasing your sensitivity to it. This heightened sensation allows greater control of your vehicle, and you will begin to see patterns and mistakes both in your driving and the setup of the car.
I shall conclude this rant, and pickup another time with regards to vehicle weight, and cover the ever so important 'driving lines'. Thanks for reading, and I warn you, this is just off the top of my head, I'm not a professional of any sort.