Powerlifters often tell me, “You just don’t understand physics! Don’t you know that bench pressing straight up and down is the easiest because it’s the shortest possible motion?” Well, I have to agree that some of that is correct. However, the conclusion is entirely wrong. Old dogma dies hard, so let me explain why I think this conclusion isn’t based in physics and our science in general. Don’t let the apparent technicality alarm you. We will keep it as straightforward and relevant as we can.
Explanation
Making the assumption that we want to limit our total work output in regards to completing the bench press, we will use the formula for work as our foundation: Work = force x distance
First, we have to calculate our force. Let’s use a 200-kg load as an example. The load obviously remains unchanged throughout the movement unless you have someone doing an upright row/assisted spot that you commonly see in the gym these days. For a bench press, the force is generated by the gravitational pull of the earth against the bar in your hands and is arrived at with the formula: Force = gravity x mass
For our example and use: 9.8 m/s x 200 kg = 1960 Newton’s
Now that we have the force calculated, let’s move on to the area of debate. This is in regards to the ‘distance’ the bar travels. Because the force is generated by gravity, the ‘distance’ used in the calculation is only that in the vertical plane. As you can see in the example below, a bar finishing at position A or B has the same total distance if they have the same starting position.
To say that there isn’t any force in the horizontal plane isn’t accurate. However, by doing the vector analysis, you will find these forces insignificant for calculation purposes. So we will leave them alone.
We need to think about ways we can reduce the work if we’re going to be more efficient and hopefully improve the lift. We then come to the conclusion that the only way to reduce the work with the bench press is to modify the starting position through arching, scapular retraction, and/or adding body mass. Let’s not forget that both amount to the same amount of work:
1960 Newton’s x 0.25 M = 490 Joules
So far what we’ve looked at doesn’t demonstrate a benefit to either bar path. So let us include Newton’s first law of motion: “An object in motion tends to remain in motion, and an object at rest tends to remain at rest.”
This law can easily be demonstrated if you’ve ever done pin presses versus hanging a bar suspended to the same height. If you’re allowed to swing or get the bar moving horizontally a little, it is significantly easier to press than when it is at a dead rest on the pins, even though they are at the same height (1).
Pushing the bar back right off the chest puts the bar into motion and makes it easier to begin transferring that force (1960 Newton’s in this example) into the bar. This can also help with areas of the lift where your force output is decreased due to biomechanical leverages. It also means that the force applied to the bar by the lifter doesn’t always have to be a constant and may be more or less than the needed force to complete the lift at various stages.
How does that possibly work? If moving the bar in both a horizontal and vertical plane with gravity only operating in one plane, you’re essentially using the “fourth basic machine—the inclined plane.” The formula for the inclined plane is derived in part from the same first law of motion.
Pushing the bar back and creating that longer ‘bar path’ nets the same work output. It actually reduces the required force to lift the bar through mechanical advantage. It may seem counter-intuitive, but it works. Although not entirely accurate, you can visualize it as lifting the weight with a longer lever. The force you need to apply is reduced, but you must move the lever in a longer range of motion.
A number of powerlifting groups and bench press specialists utilize techniques that take advantage of these principles. Although using a bench press shirt allows you more opportunity to take advantage of these leverages by exaggerating some of the dynamics, it still applies to raw benching as well. Even back in the 1980s, you found people analyzing the bench press groove and seeing results from these methods as noted in the following figure from an unverified research article:
Bar paths B and C represent those of Bridges and Kazmaier respectively, two elite powerlifters, while A represents a novice lifter. Kazmaier’s in particular shows the ‘inclined plane.’ These lifters lifted long before the advent of the bench shirt and utilized basic physics in the successful completion of their presses.
The intent of this article was to only take a quick look at the physics of the bench press and not be a ‘how to’ article on bench press technique. However, I will discuss a few common bench press techniques and their impacts (all letters refer to the diagram below).
- Bending the bar toward the feet: As you bring the bar down to point D on the chest, it is even farther away from the shoulder joint than point C. However, with attempting to bend the bar and tucking the elbows to keep the elbow below the bar, you activate the lats and anterior delts. This not only provides a platform to support the weight in this position, but it also provides the power to initiate the movement back toward the face and off the chest, initiating the press.
- Elbow tuck/elbow flare: The force is applied through the elbow. It must stay directly below the bar as you move it to the chest. This requires tucking them in toward your body, which has positive benefits as noted above and also moves the point where force is applied closer to the body. During the press, it is important to flare the elbows as the bar is pushed back to maintain the elbow position directly below the bar. If this isn’t done, an entire new set of equations come into play, with the result being the bar heading back down toward the lifters face. Elbow tuck and flare should be in direct relation to the bar position. The tuck on the way down dictates the bar position while the flare on the press is dictated by the bar position.
- Retracting shoulders: This moves the shoulders back and moves the bar finish position slightly lower as shown in positions E to F and G to H.
- Scapular depression (moving shoulders toward feet): By doing this, you move point H in the shoulder to point I. This helps move from point C to D and even lower if you have a good arch. This should be combined with rotation of the shoulders back out during the lift so that you can reach the same point F or this point will be behind your shoulders.
Again, the intent of this article isn’t a primer on technique. There is a lot to each of these steps, and frankly, many additional steps are needed to make it all come together successfully. If you wish to learn these, I suggest finding a coach or team that uses techniques similar to these. Bringing this all together, we end up with the figure on the left versus the figure on the right with the following force required.
200 kg x 9.8 m/s Sin(45) – 0 = 1385 N
The distance was shortened slightly reducing the work output as well.
1385 N x 0.31 M*** = 430 J
***Distance trigged out (i.e. using trigonometry) based on shoulder retraction and depression per above drawing.
If a similar technique was used on the straight line press, it would be possible to achieve the same vertical distance, which would result in a similar “work” output between the two styles. With the distance trigged out with a modified straight press (vertical) utilizing shoulder retraction and depression, you would achieve 0.22 M of movement.
1960 N x 0.22 M = 430 J
Note that although the work is the same in this straight press (vertical) using similar techniques, the force output required to press the bar is still 1960 N versus 1385 N.
Understand that these are made up examples with hand-drawn figures and estimated bar and joint locations, which I likely exaggerated in the examples. However, the important point is that even without the exaggeration, there would still be a reduction of some kind in the overall force output.
In our specific examples, we reduced our overall force output required to lift our 200-kg load by 30 percent. Here are the facts for comparison:
Straight (vertical) press example:
1960 Newton’s force required
490 Joules of work
Push back (inclined) press example:
1385 Newton’s force required (71 percent of the force of straight press in my example)
430 Joules of work (87 percent of the work in the unmodified straight press in my example)
So I began this article with a contentious claim, specifically a conclusion that I found false, and one that is commonly accepted powerlifting dogma. An application of physics demonstrates that the shortest possible motion isn’t the easiest or even the best if we are serious about bench pressing more weight.
Conclusion
This article is solely meant to address the forces applied to the bar when pressing back versus the straight press. It was only addressed in a two-dimensional plane and at the point of the bar. It becomes much more involved when looking at it in three-dimensional space and looking at the levers of both the humerus and forearm, not to mention the biomechanics such as how the humerus sits in the shoulder joint at different points of the lift. If you begin looking in depth in all these areas, you will find that they all support the similar bar path. If you wish to take advantage of these laws, I suggest you seek some one-on-one or team coaching at one of the strength training or powerlifting facilities around the world that utilize these techniques.
(1) On a practical note, next time you watch someone doing pin presses, watch the bar path, it often goes up an inch or so, and starts moving in the horizontal plane showing the natural tendency of the body to make the movement easier and more efficient. Physics explains why this is natural to do.
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Chris Duffin is co-owner of Elite Performance Center in Portland, Oregon, and a regular contributor to Lucharilla.com. He is an elite level powerlifter totaling 2254 lbs at a body weight of 198 lbs and has competed in three different weight classes totaling over 2000 lbs in each. 
Great article, the proof is in the test, test it yourself! Down then push back towards the rack on a slight incline I can bench more weight, than trying to keep the bar in an exact straight line, which is the shortest bar path. I use no gear and my technique is not the absolute best but for me it works as you state.
Talk about overanalyzing…
I didn’t know the bench press was an equation.
You think you can apply all that math to everybody? Too many variables with the leverages of individuals to have such a rigid outlook of an exercise.
But I guess that’s why I’m a reader and you’re a writer…
This article provides sound physics on lifting the bar. Although It starts getting away from physics when the motion of the bar is further examined. Often times in biomechanics, a researcher will examine motions in terms of joint angles and joint torques. Some motions we perform everyday, such as lifting an object off the ground is optimized to minimize work. This is a good demonstration at the beginning of the article. Every person has a maximum joint torque at a specific angle (this could be correlated to the lever discussion in the article). I would guess through more research heavy lifters have optimized their lifting motion to minimize joint torques throughout the lift. This could be validated and verified with more research. Good to see someone looking at the physics of lifting.
Cheers,
Brian J
PhD candidate, Mechanical Engineering
University of Iowa
Excellent article Chris. Well explained and well written.
Very interesting article and I won’t argue with your main point, that lifting the bar on a curved path requires less force output. But, I was startlet by a statement, you made at the beginning of your article, with the graph depicting the two different finishing positions: “As you can see in the example below, a bar finishing at position A or B has the same total distance if they have the same starting position.”
Now if you meant, that when the bar goes from the Sarting Point (let’s call it Sp), to A, it travels the same distance, as when it goes from Sp to B, I think you are mistaken.
If you draw a line between Sp and A, Sp and B, as well as B and A, you get a right triangle.
Now in a right triangle, the hypotenuse, which is the line opposite to the right angle, is always longest. SInce this is the line between Sp and A, this line is longest in the triangle and therefore, it has to be longer than the line between Sp and B. And so, the path, which the bar has to travel from Sp to B, is indeed shorter, than the one from Sp to A.
I hope I’m not mistaken here ;P
Awesome article Chris.
Maybe you could do an article for the Deadlift???
Oh, think I overread something “Because the force is generated by gravity, the ‘distance’ used in the calculation is only that in the vertical plane”
So, I missed the point xD
Sorry.
Rob,
You got it on the second post. Exactly, you primarilry only working against gravity so pushing the bar back does not increase the Work output required and doesn’t change the distance the bar is moved in the vertical plane.
Chris
SH
I have several articles I have in work. I have not come up with anything on the Deadlift as yet that can be summarized and explained in an a short article. But I will give it some more thought.
Chris
Too bad my college professor didn’t use such examples when teaching trigonometry. I might have actually passed. It makes it more applicable instead of trying to solve an equation without a need to do so. This example provides a need to do so.
Not only is Chris a fuckin’ know it all but he is a helluva welder too.
very similar to a russian article i read a while back, graphs and all. i started learning the metal melitia method of benching from some friends of mine and the ability to lock out wieghts that i was no where near able to before was all the proof i needed. as one of your readers said though it is a very involved method to use, this is not including the use of leg drive, creation of a big arch, and the generation and execution of force at exactly the right time on the press comand. in all seriousness, an elite level bench is an extremelly scientific and artistic undertaking, but thats what seperates the elite level lifters from the rest of us. not just brute strength but the display of that strength through their abilitys to move weights we only dream of with speed and grace.
Chris, thanks for taking the time to break this down!
One thing, initially, if the starting point is the same, how can the vertical height of the bar be the same (points A and B)? If they were to be the same the athletes arms would have to get longer in the case of point A. Also, interesting to note that on the novice athletes bar path, his up was longer that his down and in the two elites, their up was shorter than their down (Kaz markedly). The reduction in work adds strength to your conclusion, nice.
Something isn’t making sense. How can you discount movement (and force) in the horizontal plane? Are you implying that no force is required to move the bar in the horizontal plane? That isnt correct at all. Try rolling a 200k weight along the ground. It’s hard. There is rolling friction and it is directly proportional to the weight involved…and that same friction exists in your joints or pitchers would be throwing 180mph fastballs. I would suspect the horizontal force component required to overcome joint friction torque substanially reduces the 30% force advantage you claim.
A couple of points. First, we are in a biological system. If it takes a longer time to move the bar in a curved path (since the total distance is longer) then your body will have to do more metabolic work even though mechanical work in the vertical direction is identical. If the bench press takes longer to perform then you risk fatigue. Mechanical work would be calculated identically if the lifter paused midway through the rep, but I think we can all agree that metabolic work would be substantially higher in this case.
Second, simply moving the weight in a diagonal path does not at all decrease the amount of force required to lift it. You MUST exert 1960N of force to keep the bar in motion in the vertical direction no matter what the horizontal velocity is. If you don’t, it will fall back down. Period. As a matter of fact, moving the bar in both the vertical and horizontal direction MUST increase the amount of force you apply (however small), not decrease it. In the case of the inclined plane the total vertical force on the bar must be 1960N. If you are applying mg*sin(theta) Newtons then the plane itself is supplying mg*cos(theta) Newtons. When you bench press there is not an inclined plane assisting you, so you must be applying all 1960N.
Third, your interpretation of Newton’s third law is incomplete. Starting the bar into motion in the horizontal plane does nothing at all to help with moving it in the vertical plane. The vectors are orthogonal, meaning that changes in one have no effect on the other. The reason that starting an object that is wedged, for example, moving in one direction before moving it another is that the movement allows you to overcome static friction, which is always greater than sliding friction. Thus once the object is moving it is subject to the surface’s coefficient of sliding friction, not static. In the bench press the bar is essentially suspended in the air and you are pushing it. There is almost no friction to overcome and thus movement in one plane has no effect on the movement in an orthogonal one.
Finally, the diagrams you show illustrate why a curved bar path is superior to a linear path quite concisely. If you start at the starting point in figure 1 and push to point B, you are hardly decreasing torque on the shoulder joint at all. This makes the movement harder. If you follow a path to point A, shifting the bar toward the head at the weakest part, you are decreasing shoulder torque and increasing mechanical advantage when you need it the most. In that case you are indeed decreasing the force your muscles need to exert as you shift the bar toward your face, but the vertical component of the force applied to the bar NEVER drops below 1960N in the case of a 200kg barbell.
This is the single best post on bench pressing I’ve ever read — great article, great follow up posts and corrections.
Ultimately, I think I agree with Jake. I’d always heard that you make an arc in your press motion because of the natural rotating motion of the shoulder. So yes, I think there is less torque and friction when making an arcing motion, and hence the potential for less work done by the muscles. Still, there is the metabolic work issue. I think, in fact, the best technique might vary with weight. Think, for example, about the motion you would choose if you were competing on max reps at your body weight (assuming that’s maybe 30 reps for you). You wouldn’t probably do a whole lot of sweeping arc motions. You’d probably just start banging them out, straight up and down, about as fast as you can, to reduce the total metabolic work you do. Everytime I’ve ever seen people max out for high reps, it seems everyone naturally does that same thing. The interesting question, then, is how to properly strike the balance when doing a one rep max. Probably empirical investigation of what seasoned powerlifters do, like the diagrams you show of Bridges and Kaz, would be one of the best ways to explore that.
I agree, an article on physics and leverage in the deadlift would be great. If done, I think it should consider sumo style, not just convention. People often say ‘sumo is a more technical lift – more about the leverage’. Again, there are questions about how much one should try to swing and arc the weight versus just picking it straight up. Also, there are some folks who try to get the weight rolling before they lift it, raising the issues about vertical / horizontal plane and friction. Instead of the shoulder joint, it’s more about the hip, how much one should try to swing and snap the hips and why… Could be a very interesting discussion amongst lifting nerds.
Great article.
I do have a slight critique of your math, though… The correct formula to use would be:
work = g * M * sqrt(x^2+y^2) * {sin[arctan(x/y)] + cos[arctan(x/y)]
g = 9.8 m/s
M = mass (200 kg in your example)
x = distance from shoulder to touch point
y = vertical stroke
For a much better explanation than I can offer, see http://www.physicsclassroom.com/class/vectors/u3l3c.cfm
Basically you just skipped a step (well, two steps) when you brought the trig in, and assumed that the angle you’re dealing with is 45*. Unless your vertical stroke is the same length as the length from shoulder to touch point, the angle you’re dealing with is probably not 45*.
On another note, I see that you’re in Portland. I know that this is off topic, but do you know of a good non-crossfit gym in Vancouver or Camas? I’m a student up at WSU-V, so I get to workout there for free, but training partners are limited. Thanks.
Sorry, I forgot to post supporting numbers… It still makes the same point. This is a copy and paste from excell… sorry to be such a nerd.
A B C
Mass (kg) 200 200 200
x (m) 0 0.33 0.33
y (m) 1 0.66 0.33
Work 1960 1940.4 1293.6
99% 66%
A Straight vertical bench
B Partially shortened vertical stroke, low touch point
C Very shortened vertical stroke, low touch point
Thank you again for a great article. Sorry for the math nerdiness.
Here’s Louie Simmons’ take on this in his article How to Bench Press 500 Easy:
“The bar should be pushed back up in a straight line, not back over the face.
This requires strong triceps. This path is a shorter distance and requires no
shoulder rotation, which is also much safer. The barbell will always seek the
strongest muscle group; that’s why most push the bar over the face. Their delts
are stronger than their triceps. But it should be the reverse. One sees a lot of
shoulder and pec injuries, but seldom do you see a triceps injury. Why? The
triceps have never been pushed to their maximum, potential.”
Jake is absolutely right in his analysis above, and I’m sorry to have to say that most of the physics in this article is not correct. It may be biomechanically favourable to follow a curved bar path (I believe this is dependent on the individual and not universal), but there is no way it can decrease the amount of force you need to apply to the bar. A 200kg bar with less than 1960N of force applied to it in the vertical direction is accelerating downwards, regardless of the angle you’re attempting to move it. A bar accelerating down normally means a failed lift.
On an inclined plane, it is the reaction force from the surface of the plane itself which provides a component of force in the vertical direction. Without a physical plane there you’re still having to apply all the force yourself.
The only way to decrease the amount of work on the bench press is to shorten the vertical distance the bar travels, as you said by arching and drawing your shoulders.
Good day Chris.
Thank you for the article, BUT!
If your article has the word “Physics” in the title, you should at a minimum, get the units of measurement correct. I stopped reading as the first example equation contains the wrong units for the acceleration due to gravity (g).
The units for g are meters per second SQUARED. Could have been noted as: g=9.8m/s^2 or g=9.8m/sxs.
You list units for velocity, not acceleration.
As always, thank you EliteFTS for the articles.
Jake is exactly right, and I’m glad I saw his comment before writing my own. It’s been a long time since I earned my Mechanical Engineering degree, but these are fundamental principles.
Great effort though, and I think you’re getting people thinking.
For all the M.E’s and Physics guys, suggest having another look. The 200Kilo’s already has the 9.8M/S^2 factored in. It is a weight, and accelerating towards the earth at 1G. Albiet a misuse as Kilos are supposed to relate to Mass. Above it’s used similar to Lb-force, acceleration is already in the equation, e.g., convert Kilo to LB by multiplying 2.201…440 lbs. Repeat,it is notionally misrepresented as a weight (force) F=m x a: As used in the Physics lesson since a is gravitational acceleration, it’s already there. Hate to tell you, you’re not bench pressing 1900 newtons. (well, perhaps fig-). Cheers.
John_Squared, I don’t know what you mean when you say that 200kgs already has the acceleration due to gravity ‘factored in’, but anyone who benches 200kgs is definitely applying at least 1960N of force to the bar. In fact when you weigh something you are measuring the downward force it produces and dividing by 9.81m/s^2, so if anything that is factored out of any mass. Obviously scales are calibrated to do this automatically so we don’t do the calculation ourselves. As I said in my previous post, anyone who benches 200kg MUST be applying 1960N of force to the bar, minimum.
Jake (Sept 6) and Matt (13 Sept) have the physics/engineering analysis right. Chris’s analysis shows why it’s easier to push 1000 lbs up an incline on the hip sled than to move the same weight vertically.
Excellent discussion. I would have tpo agree with Jake and Matt on the math though.
It seems a consideration has been left oput, except partially with the Louie direct path item. The angle at the elbow changes based on bar path. There is generally a decrease in leverage efficiency at the elbow when moving the bar pout of a straight line. This is one reason why we all work tris so hard.
Deadlift study can be made from weightlifting research in translated Russian manuals. For O lifting a curved pattern is most efficient because of muscular efficiencies at varied angles. Shape is like an unfolded paperclip.