Cycling art, energy, and locomotion

by Robert P. Scott

TANGENT VS. DIRECT SPOKES.

The subject of Tangent vs. Direct Spokes, or Direct vs. Partial Tangent, is one on which so much has been written and said within the last few years that it is probably well understood in the main by all enthusiastic wheelmen, but a few points may not come amiss to the beginner. In the first place, there is no such thing as partial tangency. A tangent spoke is tangent, and that is all there is about it. A tangent is a definite thing, and means a line normal to a radius at the circumference; at least, we can accept this definition as well enough suited to the cycle art. And, in speaking of tangency, we ought rather to say tangent hub than tangent wheel, since the spokes are not tangent to the rim of the wheel, but to the hub. All cyclists know very well, nevertheless, what is meant by partial tangency in the cycle art, and I will therefore use the term. If a long spoke went straight from one point in the rim to another nearly opposite, and just touched the outside circumference of the hub in one place, it would make two purely tangent spokes. (See cut.) As, for instance, a b and c d make all together four spokes, a f, b f, d e, and c e. If a spoke runs from any point, a, c, b, or d, to any point on the circumference of the hub between f and e, it will not be a full tangent spoke. The distinctive characteristic of a full tangent spoke is that, when the force tending to revolve the wheel is applied, it pulls from the point on the hub which would recede most rapidly from that point in the rim to which the other end of the spoke is affixed. Hence, the common expression that “a tangent hub gives a direct end-pull on the spokes;” but so does any other hub, if the spoke is swivelled into it. With a direct spoke screwed into the hub, the weight of the man is sustained by a direct end-pull, and a slight power is transmitted to the rim by the resistance to flexure or bending in the spoke tending to revolve the wheel, and it will be found in practice that any hub with a direct spoke will turn independently of the rim far enough to increase the distance slightly between the ends of the spokes so as to really make an end-pull as in the tangent spoke, but evidently the hub must revolve a great way in order to increase the length a very little. Here comes in the advantage of the tangent spoke, for, in order to turn the hub within the rim, the spoke has to stretch an amount equal to the distance a point on the circumference of the hub moves. To represent this in popular terms, if the hub turns one-eighth of an inch, the spoke has to stretch that amount if tangent, whereas the necessary increase in length of the direct spoke is almost imperceptible.

Tangent spokes.

One point must not be forgotten in this matter, which redounds to the credit of the absolute direct spoke. It is that the driving strain passes through every spoke from the hub to the rim, whereas, in a tangent or partial tangent spoke, the strain is resisted by only one-half of the entire number. This defect is partially remedied by the late plan of soldering the spokes together at the points of crossing, this binding together being what really makes the tangent spokes so strong in resisting buckling, to which they were very liable before the soldering process was used. I am inclined to think that the midway or partial tangent hubs are the best, as they seem to combine all of the possible advantages, but the plan of crossing the spokes just once is, in the light of my experience, very bad, as it seems to combine the faults of both with the advantages of neither; they should be more nearly full tangent than direct if varied from the midway position at all. The small eighteen- or even thirty-inch wheel is good enough, if well made, with either direct or tangent hubs, especially in the one not used as a driver.

Old bone-shaker wheel.

The soldering of the spokes together, and other difficulties in the way of screwing them into tangent hubs, has led makers to adopt the plan of screwing them into the rim; this seems unavoidable, but is not very desirable, if for no other reason than that the wheel getting wet, the screw threads are apt to rust off and strip. With brass, aluminum, or bronze nipples, however, this difficulty can be to a great extent overcome.

Tangent wheels are as old as the industry of cycling. Starley, of Coventry, is said to have experimented and shown, many years ago, that a tangent wheel with silk spokes would resist the revolving strain on the hub equal to a direct wire spoke, and the Scientific American gave an illustration of a tangent hub in their issue of September 1, 1877.

The cross bar in the old bone-shaker made practically two tangent spokes, and pulled from the rim, so to speak, as will be noticed in our essay on hobbies.