Can a Wood Bike Be Light, Strong, and Stiff?

 
Steel and wood cross-section with logo v1.png
 

I often get asked one or some combination of these three questions: is a wood bike light, strong, and stiff? In other words: "are these frames just a novelty?"

 

In short, the answer is no, these wood bicycle frames are not a novelty. They are meant to be ridden just like any other road bicycle.

To answer the three commonly posed questions of light, strong, and stiff, I take an honest look at frame building materials by identifying the strengths and limitations of both metal and wood. And I talk about the four primary properties and principles that any frame builder considers when designing a bike. The first three of these are material properties which include: Material Density, Material Strength, and Material Stiffness (Young's modulus). The fourth is an engineering principle: Geometric Stiffness (cross-sectional shape of the frame's tubes). In the end, you will see that the real task of designing a bike frame is balancing all four of these. I'm not the only one balancing these material properties either; aluminum and titanium frame designers also consider the same things to create a light, strong, and stiff frame. I will highlight the similarities between how titanium and aluminum frames are designed with how wood frames are designed.

 

Clarification:

Before we get started, let me be clear. There certainly are benefits to other traditional frame materials (steel, titanium, aluminum, carbon fiber). Often, there are certain material properties that wood will never compete with, such as the strength to weight ratio of carbon fiber. (Carbon fiber is not evaluated in this article due to it's complexity and many variable factors (i.e. ply layups and ply strengths). Criticism of other traditional frame materials is not the purpose of this article. I am simply trying to bring you up to speed with the potential that wood offers.

 
 

Here's What You Need to Know for Our Comparison of Wood and Metal:

 

Some definitions to get us started:

  • Density: the measure of mass per unit volume.
  • Stress: force per unit area.
  • Strain: the amount a material deforms as a result of stress, written as change in length divided by initial length.
  • Strength: the ability of a material to resist applied loads [1]. Getting more specific than just strength, yield strength is the amount of stress which causes the material to deform past a point where it would spring back to its original size. Ultimate tensile strength is the amount of stress which causes the material to break.
  • Stiffness: the ability of a material to resist deflection [2]. A more stiff material will be less "affected" by force, while a less stiff material will be more "affected" by force.
  • Elastic Modulus (Young's modulus): the ratio of stress (force per unit area) to strain (the amount a material deforms as a result of stress).
  • Tension Test: a test used to determine key material properties like strength (ultimate and yield strength) and stiffness (Young's modulus).
  • Material Properties: properties inherent to the material. These include: density, elongation, fatigue limit, hardness, stiffness, shear strength, tensile strength, and toughness [3].
  • Isotropic: Metals (steel, titanium, aluminum) are called isotropic materials because they exhibit the same material properties in all orientations.
  • Anisotropic: Wood is called an anisotropic material, meaning it has different material properties in different directions. For this analysis, I will be evaluating wood along it's strongest direction (the longitudinal axis, or "with the grain"), which is also the direction of the wood grain in our bikes.
 
 

Material Properties of Wood and Metal

Density (g/cm³), Wood and Metal

Material Density

Steel [4] is the most dense material by far, with titanium [5] being half as dense as steel, and aluminum [6] a third as dense as steel. When designing a bike frame using a more dense material, more attention will be placed on how thick the tube walls are because the goal is always to create a low weight bike. Steel and titanium manufacturers will create thin wall tubes that keep the weight down, but will have butted ends that are thicker to retain weldability and strength in high stress areas of the frame [7]. The trade-off with thin wall tubes include increased susceptibility to buckling, torsion, and dents, so the tube walls can only be so thin before becoming too thin to be stiff and durable. Density comes at a cost; steel especially has the challenge of balancing wall thickness (durability) and tube weight (density). Titanium and aluminum, because they are less dense than steel, can (and must) be designed with thicker walls that are buckling and impact resistant.

 

White Ash and Black Walnut come in a distant last place with densities of 0.60 g/cm³and 0.55 g/cm³ respectively [8]. They are 13 times less dense than steel. Is this a bad thing? Not at all because this allows us to design the frame with much thicker walls that are buckling, torsion, and impact resistant. Just like titanium and aluminum, wood is (and must be) designed with thicker walls that increase strength and stiffness.

Density and wall thickness adds another extremely important constraint on dense metal tubes, which I will cover in the "Geometric Stiffness" section. This is where wood has the ability to truly perform as a frame building material.

 
 
 

Strength (MPa) and Stiffness (GPa), Wood and Metal

 
 

Material Strength

How does wood compare to metal? As you can see, wood is to be pitied most among frame building materials. In terms of strength, steel has a tensile strength of 1080 MPa, while wood comes in a distant last at 103 MPa for Ash and 101 MPa for Walnut.

Material Stiffness

How does wood compare to metal? In terms of stiffness, steel has a Young's modulus of 207 GPa, while wood comes in a distant last at 11.6 GPa for White Ash and 12.0 GPa for Black Walnut.

So hold on, why are you making bikes out of wood? At first glance, we shouldn't be. But let's take a deeper look. The test used to obtain these results (called a tension test) is testing the material's raw/inherent strength and stiffness, meaning it's maximum load bearing capacity in a small cross-sectional area [9]. So far so good. The problem with only looking at the raw strength and stiffness of a material begins when assuming larger numbers mean stronger and stiffer frames. This is not necessarily true. There is nothing wrong with inherent strength and stiffness numbers, but often people will look at these properties and instantly conclude that wood can never truly be strong or stiff.

In frame design (and engineering design in general), I need to be sensitive to the application that the materials are being used in. This means there is more to frame design than raw/inherent strength and stiffness numbers alone, however impressive or unimpressive they may be. Material density needs to be balanced with material strength and stiffness. This will show us frame strength and stiffness in a new light that makes sense in frame design. This concept is not a new one; titanium and aluminum bicycle tube manufacturers know full well that titanium and aluminum are not as strong as steel, but are also less dense than steel, so these tubes have greater wall thicknesses to compensate and create a strong, stiff frame. They're playing the same game that I'm playing to make a light, strong, and stiff frame. Below is a quick teaser on how material density is balanced with material strength and stiffness. More to come on this later in the analysis.

A stronger, more dense material like steel must be designed with thin walls to keep weight down, while a less strong, less dense material like wood must be designed with thicker walls to increase strength and have equivalent weight. 

A stronger, more dense material like steel must be designed with thin walls to keep weight down, while a less strong, less dense material like wood must be designed with thicker walls to increase strength and have equivalent weight. 

The next section graphs what I just introduced, which is strength and stiffness relative to material density. These metrics, called strength efficiency and stiffness efficiency, are the metrics that really matter in designing a wood frame.

 
 
 

Strength Efficiency (MPa/g/cm³) and Stiffness Efficiency (GPa/g/cm³), Wood and Metal

 
 

Strength Efficiency

By factoring in material density, we are led to something called strength efficiency: the strength of a material relative to its density. Put another way: how strong the material is, pound for pound. White Ash has a strength efficiency of 171.67 MPa/g/cm³ and Black Walnut  has an efficiency of 183.64, both of which handsomely beat out steel (138.82) in terms of strength efficiency.

Stiffness Efficiency

By factoring in material density, we are led to something called stiffness efficiency: the stiffness of a material relative to its density. Put another way: how stiff the material is, pound for pound. White Ash has a stiffness efficiency of 20.0 GPa/g/cm³ and Black Walnut has an efficiency of 21.1. Both fair much better in terms of stiffness efficiency in comparison to steel (26.6), but still fall short. 

 
 

So why would I consider strength and stiffness efficiency? I can use more of a less dense material (like wood) and end up with approximately the same strength, stiffness, and frame weight as steel. Pound for pound, they have similar strength and stiffness results.

That's great, you think. The wood frame can be as strong as steel, titanium, and aluminum. Now can the frame stiffness of a wood bike and steel bike be similar? Looking at stiffness efficiency alone, no. But it has the potential to be, yes. That potential yes means a frame designer has one more extremely important principle to consider, geometric stiffness, which will be discussed next.

 
 
 
1in diameter tube on the left, 2in diameter tube on the right.

1in diameter tube on the left, 2in diameter tube on the right.

Geometric Stiffness (Cross-Sectional Shape), Wood and Metal

There is one engineering equation that helps shed light onto why the cross-sectional shape of the frame's tubes are so critical. That is the Polar Moment of Inertia, Iz (a measure of a tube's ability to resist torsion). The formula for a hollow circular cross section is as follows:

Iz = π (D⁴ - d⁴) / 32     where D is the outside diameter, and d is the inside diameter [11].

This engineering equation may be slightly intimidating. The essential thing to note is that diameter is raised to the 4th power. As diameter increases, the tube's resistance to bending and torsion increases dramatically. For example, if we double the diameter of a tube from 1 inch to 2 inches (see picture), we increase the torsional stiffness 8X. The increased diameter of a tube holds extreme stiffness potential. 

 
 
 

Putting it all together

Steel has material properties that are highest in stiffness and highest in density. In order to make a reasonably light frame, minimal amounts of steel must be used. No problem; steel is strong and stiff, right? Yes. So, let's just make the walls really thin and keep the overall weight down. That's what manufacturers like Columbus, True Temper, Reynolds, etc. already do. These tubes are designed to be as light as possible by taking advantage of a large diameter with thin walls, while balancing being thick enough to resist buckling, torsion and impact. Steel, however, can only be made so thin before it becomes useless under any load or force, thus it is limited in how large the diameter can be, and how thin the walls can be. An ideal material is one where you can retain wall thickness (thus keeping buckling, torsion and impact in check) while taking advantage of large diameter tubes which increases geometric stiffness. Titanium and aluminum (and wood) do this.

Below is an illustration of what this looks like when analyzing the cross-sectional area of a steel, titanium, aluminum and wood down tube.

From left to right:  Steel  ( diameter : 38.1mm,  thickness : 0.6mm,  area : 70.7mm²).  Titanium  ( diameter : 38.1mm,  thickness : 0.9mm,  area : 105.2mm²).  Aluminum  ( diameter : 42mm,  thickness : 1.4mm,  area : 178.6mm²).  Wood  ( diameter : 56mm,  thickness : 5mm,  area : 852.5mm²)

From left to right: Steel (diameter: 38.1mm, thickness: 0.6mm, area: 70.7mm²). Titanium (diameter: 38.1mm, thickness: 0.9mm, area: 105.2mm²). Aluminum (diameter: 42mm, thickness: 1.4mm, area: 178.6mm²). Wood (diameter: 56mm, thickness: 5mm, area: 852.5mm²)

 

Below is a simple comparison of steel, titanium, aluminum, and wood. Each material's cross-section weighs approximately the same amount (within 9%). Titanium, aluminum, and wood each have a percent difference in area relative to steel. I.e. titanium has 32.8% more area than steel. Titanium, aluminum, and wood also each have a percent difference in strength relative to steel in these configurations. I.e. titanium is 10.4% stronger in tension than steel in its current configuration.

This strength calculation was simple: the ultimate tensile strength (which is the stress in tension it can endure before breaking) of steel is 1080 MPa (highlighted in a previous section). The cross-sectional area of steel is 70.7mm², which is a commonly sized down tube on a steel road bike. Using the formula: stress = force / area, the maximum force this steel tube can endure in tension is 76356 N, or 17166 pounds. Likewise, the ultimate tensile strength of titanium is 810 MPa. The cross-sectional area is 105.2mm², which is a commonly sized down tube on a titanium road bike. The maximum force this titanium tube can endure in tension is 85212 N, or 19156 pounds. This is a 10.4% increase over the steel tube from our example.

 
Steel cross-section v2.png

Steel

  • Diameter: 38.1mm
  • Thickness: 0.6mm
  • Area: 70.7mm²
titanium cross-section v2.png

Titanium

  • Diameter: 38.1mm
  • Thickness: 0.9mm
  • Area: 105.2mm²
  • % difference in area: +32.8%
  • % difference in strength: +10.4%
Aluminum cross-section v2.png

Aluminum

  • Diameter: 42mm
  • Thickness: 1.4mm
  • Area: 178.6mm²
  • % difference in area: +60.4%
  • % difference in strength: -6.9%
wood cross-section v2.png

Ash Wood

  • Diameter: 56mm
  • Thickness: 5mm
  • Area: 852.5mm²
  • % difference in area: +91.7%
  • % difference in strength: +13.0%
 

Taking material density into account is good news for wood. Wood is 13 times less dense than steel, so we can use 13 times the amount of wood for our cross-sectional area (92% more area than steel) and attain impressive strength and stiffness results because of this increased amount of wood and because of geometric stiffness, all while keeping weight nearly equal to steel, titanium, and aluminum [10]. Not only does the cross sectional area increase, but I am able to increase the diameter of the tubes to leverage geometric stiffness as well as making the wall thickness of the frame 5mm to ensure resistance to buckling, torsion and impact.

 

A Comparison of Steel and Wood in Deflection

Taking everything we've learned from above in terms of material density, material stiffness, and geometric stiffness, we're now ready to visit the simplified case study from before of steel and wood in bending. Below are the results of a wood down tube and steel down tube in bending using Finite Element Analysis (FEA). FEA is a computer based simulation tool engineers use early on in the design process to validate designs for strength, stiffness, and other parameters. Keeping the total length the same (400mm) and the total tube weight the same (.456 lbs for steel and .452 lbs for wood), the deflection of the tubes are nearly identical (0.87mm for steel and 0.84mm for wood) when a 22 lb force is applied to the free end (while the other end is fixed) Low density is turning out to be a really good thing, allowing us to leverage geometric stiffness because it is 8X more effective in stiffening tubes than the material property of stiffness alone. All while staying lightweight.

 
 

Steel

38.1mm wide (.6/.4/.6mm wall) double butted Columbus steel tubing, down tube of frame. Total deflection: 0.87mm. Applied force to end: 22 lbs. Total tube weight: 0.456 lbs.

38.1mm wide (.6/.4/.6mm wall) double butted Columbus steel tubing, down tube of frame. Total deflection: 0.87mm. Applied force to end: 22 lbs. Total tube weight: 0.456 lbs.

Wood

56mm wide (5mm wall) ash tube, down tube of frame. Total deflection: 0.84mm. Applied force to end: 22 lbs. Total tube weight: 0.452 lbs.

56mm wide (5mm wall) ash tube, down tube of frame. Total deflection: 0.84mm. Applied force to end: 22 lbs. Total tube weight: 0.452 lbs.

 
 

Summary:

The purpose of this comparison was to take an honest look at frame building materials, identifying the strengths and limitations of metal and wood. To make wood a viable frame building material, we needed to achieve a balance of the four properties and principles to make a frame that is light, strong, and stiff.

If properly designed, a wood road bike can be all three of these, with help from geometric stiffness. As an engineering principle, it is the biggest key to successfully creating a stiff wood bike. When accounting for material properties alone, it may seem that wood falls short when compared to the inherent strength and stiffness of metal. However, we see that pound for pound, wood is comparable to metals in terms of strength and stiffness. And thanks to the low density property of wood, we are able to use large diameter frame tubes to help make the frame stiff while increasing the tube wall thickness to add frame durability and strength.

 

Notes and References

[1] Materials Handbook / George S. Brady, Henry R. Clauser, John A. Vaccari. N.p.: McGraw-Hill, 2002. 1096.

[2] Materials Handbook / George S. Brady, Henry R. Clauser, John A. Vaccari. N.p.: McGraw-Hill, 2002. 1096.

[3] First, this is not an exhaustive list of material properties. Second, I am consciously lumping in a physical property (density) with mechanical properties (elongation, fatigue limit, hardness, stiffness, shear strength, tensile strength, and toughness) for the sake of conversation and all of these which are considered more generally material properties.

[4] Reynolds 725 Chrome-moly Steel Bicycle Frame Tubing, http://www.reynoldstechnology.biz/materials/steel/s-725/

[5] Reynolds 3-25 Titanium Bicycle Frame Tubing, http://www.reynoldstechnology.biz/materials/titanium/t-3-2point5ti/

[6] Reynolds 7005 Aluminum Bicycle Frame Tubing, http://www.reynoldstechnology.biz/materials/aluminium/a-7005/

[7] https://roadbikeaction.com/features/rba-features/ask-rc-butted-titanium-tubes-and-their-effect-on-frame-stiffness

[8] Forest Products Laboratory. 1999. Wood handbook—Wood as an engineering material. Gen. Tech. Rep. FPL–GTR–113. Madison, WI: U.S. Department of Agriculture, Forest Service, Forest Products Laboratory. 463 p. https://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr113/ch04.pdf

[9] The tension test measures stiffness in the same size specimens with the same cross sectional area (also called section modulus). Look at the equation used to determine stiffness: stiffness = stress / strain, where stress is measured as force divided by area. This area in a tension test is very small, and most notably works independently of material density. When designing a wood frame, I don't need to worry about maximum load bearing capacity in a minimum amount of area because I am not constrained by this minimum cross-sectional area and thus by extension, material density. Rather, my constraint is overall frame weight ‑ I am trying to make a wood frame weigh the same as a lightweight metal frame.

[10] The strength and stiffness properties do not change when increasing the cross-sectional area (i.e. wood has an inherent strength of 103 MPa and stiffness of 12 MPa no matter what the cross-sectional area looks like). But when increasing the cross-sectional area of a wood specimen, it can carry a larger load, proportional to the increase in the cross-sectional area. Remember, our goal since the beginning is to design a wood frame that is comparable in weight, strength, and stiffness. Thus, to achieve our goal of a lightweight frame comparable to metal in terms of strength and stiffness, we need to take material density into account, which allows us to increase the cross-sectional area of the tube.

[11] This formula is for a hollow circular cross-sectional area. The cross-sectional area on our frames is not exactly circular (they have a more aero profile than they do circular). Thus, the polar moment of inertia for hollow cross-sections is intended to be used as an approximation to get the point across that the diameter of tubes is critical to increasing stiffness.