Aerials, Apparatus, Daly, Pumpers, Rescues

Apparatus Operation: Curves

Issue 6 and Volume 21.

I’m sure everyone has had this experience: You are riding shotgun on the way to a call, and you’ve thrown your helmet onto the dashboard so that you can read the map book.

As the fire apparatus operator rounds the curve, your helmet starts to slide across the dashboard and nearly goes out the window before you are able to grab it. That was close; you would have missed a job if you had no helmet to wear. The sneaky culprit that almost stole your helmet was inertia, and it’s another key concept that professional fire apparatus operators must understand.

What most drivers don’t realize is that every curve in the road has what’s called a “critical speed.” If you take the curve faster than this critical speed, your vehicle will break traction and continue in a straight line instead of negotiating the curve. As a result, the vehicle will travel off the road and crash.

Outside Forces

Fire apparatus operators must understand that as we round a curve, there are two major forces working on our vehicle. The “bad” force is centrifugal force, which makes our vehicle want to continue in a straight line off of the roadway. The “good” force is the traction between our tires and the road surface.

As long as we have more traction than centrifugal force, our vehicle will hold the road, and we will make it through the curve-no questions asked. However, when we drive too fast for the road conditions, we allow centrifugal force to overwhelm our tires’ traction. When this happens, the vehicle breaks traction, and we lose control.

The speed at which we lose control depends on three major factors: the radius of the curve (how sharp it is), the coefficient of friction of the roadway (how “sticky” it is), and the superelevation (“bank”) in the road. Problems arise as your speed increases, the sharpness of the curve decreases, or the stickiness of the road decreases with bad weather.

When you think about it, the curve and bank in the road will never change; however, the stickiness of the road will change based on the weather. As the road gets slicker with rain, snow, or ice, the critical speed of the curve will go down.

Critical Speed of a Curve

Let’s go back to the example of your fire helmet. As the fire truck rounds the curve, the traction of the tires on the dry road surface is more than the centrifugal force trying to make the fire truck continue in a straight line. In this case, the fire truck maintains traction with the road and safely negotiates the curve. However, your plastic helmet is resting on a freshly polished, vinyl dashboard. The “stickiness” that is keeping the helmet from sliding around is considerably less than the stickiness between the tires and the road. In this case, the centrifugal force experienced as the vehicle rounds the curve is more than the coefficient of friction between your helmet and the dashboard. As a result, your helmet breaks traction with the dashboard and tries to keep traveling in a straight line, attempting to exit the window.

The reason for this can be shown scientifically. To figure out the critical speed of a curve, you need only three things: the radius of the curve, the coefficient of friction of the roadway, and the superelevation of the road. By plugging these three values into the following formula, we are able to calculate the critical speed of a curve.

3.86 √ R × (f ± e)

“R” is the radius of the curve. The roadway’s coefficient of friction is represented by “f,” and “e” is superelevation of the roadway.

As with stopping distance, the purpose of learning this formula is not to freak you out. The purpose is to demonstrate that nowhere in the formula does it say to rate yourself on a scale of 1 to 10 and multiply or divide by the number of years you’ve been driving or plus or minus 12 if you are en route to a working house fire vs. an automatic fire alarm. The kid driving for three months will exceed the same critical speed as the savvy old veteran who has been driving for 30 years. You can’t beat Mother Nature.

Effects on Drivers

So how does this affect us as drivers? It means that as the curve gets sharper, or the road more slippery, the critical speed goes down. In other words, if it’s raining, you can’t drive through the curve at the same speed as if it were dry. Here’s why.

Let’s consider a curve with a 150-foot radius; this is a pretty common curve for most of our districts. On a dry day with dry asphalt and a coefficient of friction of 0.9, the critical speed for the curve is 44 miles per hour (mph). Drive faster than 44 mph, and the truck will fail to stay in the travel lane and safely negotiate the curve. Instead, the vehicle will continue to travel in a straight line and strike whatever happens to be along the roadside.

Now let’s say it’s raining and the coefficient of friction for this same curve is 0.4 because of the slicker roadway. This “more slippery” road condition will lower the critical speed to 29 mph. The critical speed of the curve dropped from 44 mph on the dry day to 29 mph on the wet day. As we can see, the critical speed fluctuates with the weather-another important point that professional apparatus operators must come to understand.

High Centers of Gravity

As apparatus operators who are driving vehicles with high centers of gravity, it is important for us to understand what else centrifugal force is doing to our vehicles. As we round a curve, centrifugal force begins to push the weight of your vehicle onto the outside tires, especially the front passenger side tire. This weight shift causes the body of the vehicle to deflect down onto the suspension (shocks and springs) and thus shifts the center of mass toward the outside of the curve. In most cases, especially when dealing with a standard automobile, this weight transfer has little effect on the vehicle: It safely negotiates the curve, and you continue on your way. Sometimes, if you are going too fast for the curve, the weight of the vehicle will shift onto the outside tires and you will start to hear your tires squeal. Again, most drivers let off the gas and continue on their way. But, what about when you are driving a vehicle with a high center of gravity-namely, a fire truck?

When you are driving a fire truck through a curve, critical speed is not the only thing you have to worry about. A vehicle with a high center of gravity is less stable during cornering situations. This is because the center of mass shifts as the suspension deflects down and out in the direction of the centrifugal force. If the center of mass shifts too far, the vehicle may tip over. Or, the vehicle might not tip over completely but may drift off the road just enough that the driver is forced to recover and try to get the wheels back on the road.

This scenario is another common cause of fire apparatus crashes as the driver overcorrects and causes the fire truck to rollover in the opposite direction. This is what is known as an “induced yaw.” In other words, by turning the wheels too hard to correct the vehicle’s path of travel, the vehicle is put in an artificial cornering situation that it is going too fast for. As a result, the vehicle “trips” as it rotates around its center of mass and ends up rolling over.

Another factor that operators must consider when rounding a curve is that most fire trucks carry several hundred gallons of water. Not only do you have to worry about a high center of gravity and the weight of the vehicle shifting to the outside tires, but you also have to worry about the water “surge” in your tank. This surge of energy will also add to the forces that are trying to tip you over or at the very least cause you to drive off the road. This is one of the main reasons that water tankers (or tenders) are the most common type of apparatus involved in serious rollover crashes.

As professional apparatus operators, we must remember that Mother Nature is constantly trying to push us off the road. Because of this, we must respect the dangers of driving our apparatus, especially on emergency calls. We must be familiar with our districts and know where the curves in the road are. We must slow down well in advance of these curves and take them at a safe speed. Midway through the curve is not the time to realize you’re going too fast-by then it will be too late.

CHRIS DALY is a 25-year veteran of the fire service and a full-time police officer who specializes in the reconstruction of serious vehicle crashes and emergency vehicle crashes. He developed the “Drive to Survive” training program (, which he has presented to more than 14,000 emergency responders across the country, and lectures nationally on preventing emergency vehicle crashes. Daly has a master’s degree in safety from Johns Hopkins University, is a Fire Apparatus & Emergency Equipment editorial advisory board member, is a contributor to Fire Engineering, and has presented at FDIC International for the past 10 years.