Design Factors for Dynamic Loads

What are Dynamic Loads?

In simple terms, a dynamic load is any load that moves, changing magnitude or direction over time. Loads in a static system are constant and unchanging. Newton’s Laws of Motion reconcile the equilibrium in static systems easily.

For the purposes of this article, you should consider that the term “dynamic load” refers to any load in motion, changing velocity or direction. Shock loads, impact loads and vibrational loads can all be considered dynamic in nature, but are not the same.

The Basics.

One of the most basic equations in physics is F=ma. Force is equal to mass times acceleration. In this equation, any change in values for mass or acceleration effects a proportional change in force. The acceleration component to this equation implies that time is a related factor; indeed acceleration is the time rate of change in velocity. When an object accelerates or decelerates, its change in velocity over time is important, but F=ma considers only the instantaneous force of an object’s inertial mass relative to its time rate of change, when accelerating at a fixed rate. Simplified, if an object is accelerating, then it has a force applied to it. On the other hand, if an object is not accelerating (either at rest or at a constant velocity) then it has no force acting upon it. These are basic precepts of other formulas, which calculate kinetic energy, force of impact and energy dissipation.

It’s About Time.

We tend to think of dynamic loads in terms of a falling object, because it’s relatively easy to relate acceleration “a”, in F=ma, as the force of gravity. However, if the direction of motion is not vertical, then we may not fully consider dynamic loads appropriately, mainly because gravity is less intuitive when motion isn’t vertical or down.

What’s more important is not so much that an object changes direction or that it stops, but rather how quickly it does so. It’s not the fall that matters, but the sudden stop at the end. Timing is everything – if I can stop my falling body over a less sudden time span of a few seconds, then the stop at the end becomes less critical and certainly less messy. Hold that thought…

E_k=1/2mv² is a simple formula for kinetic energy. Kinetic energy is measured in Joules – the work expended by applying a force of 1 Newton (or 1 Kg·m/sec²) over a distance of 1 meter. A Newton (N) is the force exerted by gravity on an object with mass (m). If I weigh 100 Kg and that weight is the product of my mass times gravity, then I have a mass of 10.2 Kg and with the help of gravity, I exert a force of 10.2Kg x 9.8 m/sec2 =10.2*9.8 Kg·m/sec2 = 100N on the earth’s surface. F=ma.

This can be similarly expressed in terms of momentum (P) = mass (m) x velocity at impact (v), therefore P= 10.2 N(4.4m/sec) = 44.9 Kg·m/sec, at that instant in time. Momentum isn’t a force per se; it’s a product, but it can be related to Newton’s Second Law and therefore to inertia. In this equation, mass (m) refers to inertial mass or a proportionality factor relative to an object’s tendency to resist changes in motion. Where are we headed with all of this?

Back to my falling body example: think of impact in terms of what stops my fall. If I hit an airbag, call it a stunt; if I hit concrete pavement, call that messy. Intuitively, this should translate into how much time it takes to stop – how quickly the kinetic energy is absorbed or dissipated. Now we’re getting somewhere, and it’s about me!

Time for a Change.

Newton’s Laws suggest that any change in direction is the result of a force having sufficient magnitude to effect such a change. When designing a system to accommodate any load we must consider a design factor so that the affected object is strong enough that it doesn’t fail or break when subjected to an opposing force. In the simplest of terms it is stopping the object while it’s in motion. Think about it for a moment – a roller coaster on a curvy track, Peter Pan on the end of a wire – to move requires force and to change direction or stop requires opposing force.

In the case of a roller coaster, the car must be designed such that the change in direction caused by the wheels in contact with the track doesn’t cause the wheels to become dislodged or to break. So too in the case of a human on a wire, the forces exerted to stop motion must not only consider the component strength of materials used in the system, but must also consider the maximum forces a human body can tolerate without being damaged. When the system of forces is not appropriately considered, the results can be deadly. In simple terms, if the roller coaster car or the human being is caused to change direction too rapidly, the reactions from the inertial forces can be significant. If the change in vector forces is gradual, the dynamic loads are greatly reduced.

The Pipe Batten.

Let’s begin with a reminder about how a manually operated counterweight system works:

A batten load is counterbalanced by an arbor counterweight, ideally in perfect balance, but generally to within 50 lbs of equilibrium under normal operating conditions.

When the operating line on this theoretically balanced line set is pulled by the operator, causing the arbor to move up or down, there is an associated reaction through the wire rope lift lines to the batten, so it moves up or down. The force to start motion is usually very gradual, so too is the force to stop motion (gradual through feathering the operating line, presumably through one’s gloved hands). This manual action inherently provides a bit of a safety factor, because the amount of friction that can be applied using one’s gloved hands is directly related to one’s ability to withstand the heat generated by such friction. All of this is possible because the load of either the dynamic motion or the imbalance in the system can be controlled by the friction generated by a gloved, human hand and returned to near equilibrium with little effort.

On the other hand (no pun intended) if the load imbalance is more than the human hand can tolerate and more than operational friction can resist, then forces remain imbalanced and motion continues until something acts with an opposing force on whatever is moving. In one example that almost never happens, counterweight is removed from the arbor while the batten is at high trim and the friction caused by the rope lock or the “uncle buddy” is released. A load imbalance occurs, the equilibrium is upset and motion is inevitable. To stop this motion, Newton’s Laws say we need an equal and opposing force. In this case, it’s the arbor stops (also affectionately known as crash bars) which establish a finite, somewhat effective limit of motion.

Trust me on this: a runaway arbor does not like to work within limits. In the span of a second or two, and with enough adrenaline, the operator can jump away fast enough, instinctively taking the age-old expressive posture that only means one thing: “I didn’t do it, I swear!” Fractions of a second later the now runaway arbor decides it still doesn’t like working within limits – it hits the stop, which tries to resist with an equally opposing force, the result of which usually causes things to break. Shocking, I know.

There are several factors that contribute to this little mess: the area of impact is very concentrated, the force of impact is distributed among very few components, the materials used for stops are generally not at all resilient (steel angles, hardwood bumpers and really big bolts), and the deceleration and stopping time required to achieve the required equilibrium of forces is extremely short.

Someone might have specified a 5:1 design factor for the steel in this system, but that was probably only applied to normal design loads occurring under normal operating conditions. It didn’t and shouldn’t account for accidental loads such as dropping a fully loaded batten from high trim.

Back Where we Started.

These same principles apply when selecting a brake for a motorized hoisting system. If the load is a structural frame, the frame has to be designed to tolerate being stopped in whatever the brake’s design activation time requires. In researching dynamometer samples of dynamic braking force tests, we’ve seen shock load factors due to braking ranging from as low as 1.5 to as high as almost 4, depending upon the load and brake solenoid reaction time.

In motorized systems used to fly performers, these dynamic loads (due to braking and to changes in direction) can become critical to performer safety. In a fall protection system, the maximum arresting force permitted to be transmitted to the person wearing the harness must not exceed 1,800 lbs. Consider that a 200 lb person dropping 4 ft on a Self-Retracting Lifeline with a 2 in stopping distance and no shock absorber generates about 4,800 lbs of arresting force, and it’s still messy!

The concepts of dynamic loads, of inertial mass, of time rate of change in velocity, all find roots in F=ma. Remember, this is intended to be a highly simplified discussion of dynamic loads, hopefully just enough to whet your appetite. Don’t try this at home folks!